1.

The weight of a body at the centre of the earth Is

(a) Zero
{b) Infinit e
{c) Same as on the surface of earth
(d) None of the above

2. The centripetal force acting on a satellite orbiting round the eanh and the gravitational force of earth
acting on the satellite both equal F. The net force on the satellite Is

(a) Zero
lb) F
(c) F 2
(d) 2 F

3. 1r the earth stops rotating. the value of 'g' at the equator will
(a) Increase (b) Remain same (c) Decrease (d) None of the above

4. As we go from the equator to the pales, the value of g

(a) Remains the same

(b) Decreases
(c) Increases
(d) Decreases upto a latitude of 45•

5. The weight of an object In the coal mine, sea levei, at the top of the mountain are W 1, W2 and W3
respectively. then
(a) W3> W2 <Wl (b) W3= W2 =Wl (c) W3< W2 <Wl (d) W> W2 >Wl

6. If the earth suddenly shrinks (without changing mass) to half of its present radius, the acceleration
due to gravity will be
(a) e/2 (b) 4g (c) g/4 (d) 28

7. Spot the wrong statement : The acceleration due to gravity 'g' decreases 1r
(a) We go down from the surface of the earth towards its centre
(b) We go up from the surface of the earth
(cl We go from the equator towards the poles on the surface of the earth
(d) The rotational velocity of the earth is Increased

8. Radius of earth is around 6000 km. The weight of body at height of 6000 km f rom eanh surface
becomes

(a) Half (b) One-fourth (c) One third (d) No change

9. A body weight 500 Non the surface of the earth. How much would it weigh half wav below the
surface of the earth
(a) 125 N (b) 250 N (c) 500 N (d) 1000 N
10. The masses of two planets are In the ratio 1: 2. Their radii are In the ratio 1: 2. Th,; acceleration due
to gravlrv on the planets are In the ratio
(a) 1 : 2 (bl 2 : 1 (c:) 3 : s (d) 5 : 3

11. In a gravitanonal field, at a Point where the gravitational potential Is zero

(a) The gravitational field Is necessarily zero
(bl The gravitational Reid Is not necessarily zero
(c) Nothing can be said definitely about the gravitational field
(d) None of these

12. A particle falls towards earth from lnflnlrv. It's velocity on reaching the earth would be
(a) lnfinirv (b) 2gR (c) 2 gR (d) Zero

13. The escape velocirv for a rocket from earth is lLl km/sec. Its value on a planet wh,ere acceleration
due to gravity is double that on the earth and diameter of the planet is twice that of earth will be In
km/sec (a) 11.2 (b) 5.6 (cl 22.4 (d) 53.6

14. The escape velocity from the earth is about 11 km/second. The escape velocirv from a planet having
twice the radius and the same mean densirv as the earth, i s
(a) 22 km/sec (b) 11 km/sec (cl 5.5 km/sec (dl 15.5 km/sec

15. Select the correct statement from the following

(a) The orbital velcocirv of a sat ellite increases with the radius of the orbit
(b) Escape velocity of a particle from the surface of the earth depends on the speed with which it is fired
(cl The time period of a satellit e does not depend on the radius of the orbit
(d) The orbital velocity is inversely proportional to the square root of the radius of the orbit

16. If a satellite is orbiting the earth very close to Its surface, then the orbital veloclrv mainly depends on

(a) The mass of the satellite only (b) The radius of the earth only (c) The orbital radius only (d) The mass
of the earth only

17. Orbital velocity of an artificial satellite does not depend upon

(al Mass of the ear th (bl Mass of the satellite (cl Radius of the earth (di Acceleration due to gravirv

18. The lime period of a geostationary satellite Is

(al 24 hours (bl U hours (cl 365 days (dl One month

19. The welSht of an astronaut, In an artificial satellite revolving around the earth, Is
(a) Zero (bl Equal to that on the earth (c) More than that on the earth (d) Less than tha;t on the earth

20, Escape velocity on the earth

(al Is less than that on the moon (bl Depends upon the mass of the body (c) Depends upon 1he direction
of projection (dl Depends upon the height from which It Is projected
 Gravitation

Gravitation
Newton'• Law of Gravitation (b) Z.ro
Cc) 27 ,, 10 ,. Cd) JnJt 10: 1
•• A••tdlltoof thc ..rth L, rc1'Uhi ng in• dm1lnr orbit "'th
a unifom1 S)k"l-d u. Ir the grnvil11lio1W force imddenly 8. Om,itntional 11\lL<S Is proportlocuol to gm,iblllonol
disoppo•"'• tho S<llolllte will IAll~IS 1911z: AIF.F.1'. aouol IAIII\IS 1.,.NI
{•) Continue to "'""' with wloclty o •long the origlnol C•l l'idd (b) rorco
ol'blt (c) Intensity (d) !,II olth"""
(b) Mow with • "'lotity o. tnngcnti.Uy to the origlnnl 9. 111c g-nl\itation.11 fon.."C bct..,.,•ttn two poinl nmssc." '", nnd
orbit
' ,. j
"': "l~rahonrL'IJ;VCOuf
L.. F• i '"1'~:h
(<) full do\\11 "ith Increasing wlodty r
(d) Ulllmntoly romc lo rest sonll"'hcn:on the 01igin•l 111c ,-on51ant k ICPMT '""31
01·blt C•l DL-p<-nds tXll')~k m of unit. ool)·
(b) lk'P"llds 011 medium hcl,\'C<11 mn.<.= only
2. l11e "lTIIO.'Phere b held to the cnnl1 by I IIT 191111)
(c) Popend, on bolh (•l nnd (b)
(•) Win<L< (bl Gmity
(cl) Is indq,o:ndcnt ofbolh (11) .nd (b)
(c) Clou,b (d) l'\onedthc ohow 10. l1lc dist•= of the t'Cntl\,s o( moon •nd enl'lh is 0. The
l1lc weight ol n body •l the C'1\ U'C of tho rnrth L, mn.,s o( earth is 81 Llm,-s Uie m.1.~• orthe moon. At wh.,t
IM"MC 1911111 clislnnce Imm the conlre of thc eurth. the grn.;tation•I
force will be n:ro !Rt••:Y ,..,..,
(•J Zero
(b) lnlinllc l•l D (b) lD
l
(c) S.ime n."on the: surf.ice of onrth
(c) 4/J (cl) •n
(d) Noncoftho•bo," ] 10
4. II the dl,1a11tt bctwt"en two ma.<S<c< ls dn11bled. tbt u. 1'hc ccnlripdnl ron..., •ding on a "1lcllite orbiting round
i;,n1il11lional nltrndion bctwc"Cn them the c1111l1 and I.he gravit11ti<••d Ion:,, of ear1h ncting on tho
lct•~rr 1973: AMU(M od.1 ...... , ,111lcllite bolh equal f . The nd force on the sntelllte i<
!•) Is doubled (b) llcromes fo<ir l1 mes IA&iu,.....,1
(n) 7.cro {b) f
(c) Is r<sluced to lwf (d) lsredocc<I to II qnnl'ter
5- ll'hlch of the lollo,,in~ ls the c1id<m'C lo ,how !hut lhtn, (c) f-.fi (d) 2f
must be n fOft.'e llding on enrth and dirtt1ed towmTIS the 111. Mns.< M iJ dhicl<-d into lwo pnrt.<.r M oncl fl - ,t' l.1/ . for•
:nm ~,;vcn "4.1'3ration. lhe ,·nine or.,·for which the gm,itati0041
IAIIMS 19801 altrnt1tOn bet'"wn the t·wo pk."'CCS becomes mnximum i~
(•l lk'l'inlinn ofthe (tolling t, .il,-. ,.,..-.nls ca.<t I F.AMCt:Y :to<11 I
(b) Revolntio11 o(the e.1rth round the sun (n) .!. (h) !
(c) Phenon,eoon ofdoy nn~ night ' 5
(c) 1 (d) 2
(d) Appnn,nl n"11ion of sun i<•ind the earth
13. 111e force, o/ grmitation is IAIIMS2c>c>2I
6. 1\,o 1>•1'licles of '"!""I ma,;, go mund • circle of l'lldius R
under the action of t.hrir mutual grmitntionnl att1'11dian. (a) Rq>uw,-e (b) FJ«trostutlc
~ :ipccd of each puticle is ICBSF. rMT ,w:,:; krMT :irvu:,J (c) Con.scn11th-c (d) Xon-..-on.~rvl1tin:

C•l ,_ _1
lR(a;
11 Cbl ,.• Jc..
1R 14. Two sphere ol ma.ss m ond Mare •ituat.ed in nir and the
gra\~lntional fon-e betv.'Ccn them tS F. The l ]lltcc around
(c) v=.!. J G'm
l R
(d) •·•Pf the m•sses ls now filled with • liquid of specific grn1ity 3.
"°"'
11,e gr111itationnl for<'<> will he lca.qF. t•irr wo3l
7. l11e eonh (mas.• - ~• 10" .Ii:>) """""" round U,e sun (n) f (b) f.
J
\\ith angular \'r:lotity .:! x Io -, nu/ I s in a cim1lnr orbit of
f'
mdiw 1.5 )( 10• ,,.,. . The force exerted by the sun on the (c) - (d) 3f
c:uth in newtons,, is
•
ICBSE rm '""5' AFMC ......, l'l,. "1T2003]
15. Which of the follll'ling statements about the gravitatimlll (d) ln ,'3CUUIII lhcre is resi!lrulre <ifl'ffll to lhe motiln or
ronsl:ml is tru, (Mnla PET2003J the bod)· and this resistance d,pends on the mass of the
(a) It is a forct' holy
(b) It has no wiit 7. When a body is taken from the equat<r to the poles. it,
weight )EAMCET 19;8)
(c) It has same ,11hie in all S)>lems o( unit.
(a) Remains constant
(d) It depends on the nlue of the masses
(b) Increases
(e) It does not depend m the nabm, of the medium in
(c) Decreases
which the bodies are kept.
(d) Increases at N-pole and <k:e al s-po·le
16. l\vo identical solid ropper spheres of radius R placed in
contact v.ith mch other. The gnnitational attracton 8. A body of mass m is taken to the bottom of a deep mine.
Then (NCERT 1982)
between them isproportiainl to Junia r1IT1005J
(a) R' (b) R-'
l•J It,"""" increa,es (b) 11s ma._.., deacases
(c) 11" "--eight ioaases (d) lbnght dem,ase:,
(c) R< (d) R·•
9. A spherial planet far out .i n spoce ha, a mass .110 and
AccekH"atlon Due to Gravity diameter L\ . A particle of mas, m falling freely ne.ar the
su1face ol this planet 1>ill experience an acceleration due
J. Wei_ghtlessness e.'<perienred while orbiti~ the earth in to gra,itywhicb is equal lo )MP nlT 1911?: DPIIT:aooa]
spoce-ship, is the result of ) NC£1lT 19)11: DPMT 1981)
(a) Inertia (b) :IL'Celmltlon l•J GM0 1 ~ (b) 4mG.110 ii)[,
(c) Zero grll\il)· (d) f""' fulltowards earth (c) ◄GJ/0 I 4 (d) Gm,1/ol Di,
If tlue change in the ,-.Jue of· g' al • height h abo,,. the 10. If the. earth stops rotating, the ,-.Jue of' g' at the equator
surf.tee or the f.'llrth is the same as at a cl!'pth x below il. v.ill
then (both .t and h being much smaller than the radius of
[Cl'MT1986)
the earth) [NCEICT 1.9831 BHU :IOOI)
(a) Increase (b) Remiin same
(a) ., = /1 (b) X = 1/,
le) Decrease (d) Nooe of the above
(c) ., = -," u. The mass and diameter of a planet hove twice the ,-.Jue o(
the w11espo.xling parameters of earth, Acc<leratioo due
3- lbe time period o( a simple JJendulum on a freely mo,ing to gravity on the surfare of the planet is
artificial satellire is [Cl'lff 1"34; AFMC 1001.J [SCERT t9?11 Ph. PMT2.000J
(a) Zero (b) 2 sec (b) 4.9 m 1,cc:
(c) 3 sec (d) ln6nite
l\vo planets ha,1: the SIJllC awrage dmsily bul their radii (r) 980 ,,n ,cc~ (d) 19.() m l ,cc 1
are R, and R: . If accelerntion du, lo gra,,ity on the,r u. As we go from theequal<r to thepoJ...,, the valile of g
planets be . , ond &, respecti,'el)", lblSl )AJIMS 1985) (CPMT 1975: AFltC 111<15: AFMC1004)
l•J Remains the same
(a) .!lJ. = ~ (b) Dccn,a,es
g1 R1
lc) Increases
(c) .liJ.=4Ri
Kt 13.
(d) Decreases upto a latitude of 45'
forceofgra,ityis leastat [CPMT1991J
An ~ron ball and a wooden ball of the same radius are (o) lbe ,..,..tor
rdea,ed from a height 'h' in ,11cuum. The time taken IJ)· (b) lbe poles
both of thomtomidt tbeground is (c) A point in between oquotor and any pole
[NC£JtT 1975: AFMC 1998) (d) Noneofthese
(a) Unequal (b) E.uctl)· equal
14. The radius of the earth is 6400 km and i; = IOm I = ' . lo
(c) Rougblyequal (d) Zero
order that a body of 5 kg weighs zm> at the ,equator. the
6. The correct answer to above que.ilion is based on angular sp,«I of theearth is IMP PMT 1985)
)NCERT1975)
(a) 1/ 80 radian/s« (b) 1/ 400 radia.n/s«
(a) A<.-celeration due to grmity in \.KIJurn is same (c) 1/800 radian/sec (d) 1/ 1600 radian/soc
irrcspmni, of si:ze and mass of th• body
15- The value of·g· at a particub1..r point is QJl nr I :.1 . SUppose
(b) Acceleration due to grn,ity in '11CUU111 depends on the
moss of the body the earth soodenly shrinks uniformly lo half its present
(c) There is no .....-elcration due to gmity in ,11cuum size without kmng nny mrw. lbe ,-aloe or ·g· ot lh, same
point (assuming that Ute distm,-., of the point from the
centre of earth doe, not sh1ink) .,;u now be
 Gravitation

[NCEKT 1984, DP&ff 1999) 23. If the earth rotates faster than its present speed. the
(a) 4.9m l sa:' (b) 3. 1 "' , scc 1 weightcl an ot;ect will (ltlU'yunaCEE 19961
(n) Increase al the equator but remain unchnnged •t the
(c) 9.Km i = ' (d) 19.om I K <l poles
16. If R is lhe radius of the eru1h nnd g the ocrelcratlon due to (h) Dccreasr at the equnlor but remnin unchnngcd at the
grn1ity on the earth's ,s11rf11t,:, the m<>,.n d,-n.,lty of 1hr poles
earth L< I9t¥1lfd!H•NIJ,!lfll\\!lkl'fflllt ~IIA"IHll d,~w nsc nt the
)Ill c:•:r (Mod,> '""'" cast: r~rr 1'l<ls l poles
(a) ; ,,C/ ,,R (h) J tdl ••-<; (d) Remnin unchanged nl the equator but inc1·ca.<c at the
(c) Jg / ;,:JIG (d) 111/G l! G poles
17. The w• ighl of an obj,-ct in the coal mine, sea le\·el, al the If the eJ!rtb J1wld~~- shrink., (without changing mass) to
half of its pres,nl radiu.1, the ..-ulmtion due lo gra,ity
top of the mountain llff II(. If'! nod U-1 respectively,
>1ill hc: 111x11 ,..,,,-1
!hen
(a) g/ 2 (b) 4!I
(EAMCET 19901
(c) g/ 4 (d) 2g
(a) lfi < 11, > 11; (h) l 'i : 11; : n;
2.5. The 1I10011°s radius L< 1/ 4 that a( the earth and its mass is
00 ~ <~ • ~ 00 ~ >~ >~ t/80 times that of the earth. If g represents the
18. The radii of two pl.,ne(5 are respecfu-.ly R, and R, and accelernlion dur to grol"ity on the surface of the earth,
that oo the surf0t.-e of the moon is
their densities are 1e;p,.-ctiwly "' and P:. The ratio of
MP PET2000, ot: R.PET2000: Ph. PET2001J
the ~lcrntions due to gravity at thcir surfaces is
(o) 9/4 Ch) g/ 5
IMP PF.I' .... I
(<) g/ 6 (d) g/8
26. II is the m1L< of the l'<lrth and .., i,, iL< nngular wlocity
,ind ~.. is the 1-.Juc of g nt lhe poles. The ,-ff,'<ti,-e ,-.lur of

.
(c) ,:1 : >-:!
• R1PJ : Ru, {d) ,:1 : ,:: • R">, : Ru'!
g 11t tho latitude l • N>' will be oqu.,I to
19. 1be mnss ofthr orth ~ 81 times that o( the moon nnd the
radht• of lhe earth i., 3-5 times Uu11 of lhemoon. The rntio (a) g --I Rtti l '
(h) G, - -Rm·
,. 4
of the aereleratioo du~ to grn,i ty at the surfa,-e of the
moon to thnt at the surf,ce of the earth i., [~rr P~rr •-I (c) g, - R a1! (d) X, +4I RilJ·'
(a) 0. 15 (h) 0.Q.j
(r ) 1 (d) 6 27. The depth d at which the ,-.Ju, of acceleration due to
2.0. Spot the wrong stitement:
grmity becomes .! times the ,-,i1.., at the surface, is [R:
The •=leratioo due, to gravity ·g· cleanses if n

(a)
••••I
(MP PMT
We go down from the surfiwe of lhe earth tmmrds b
radius of the earth] (MP PMT 1999: K•nla P&ffll00$)

(n) R
centre
(h) We goup from the.!Urfaceof threuth
•
(<) We go from the equator i.-nls the pole• on the
,urr- of the r.U.
(c) ,~ (di 11(.,~1]
(d) The mtationlll velocity ortlw ••rth i.s Increased 2.8.Al what height over the earth"• pole, the f,w fall
2 1. Which cl the i>llowingsl1tcmllli. i., tn1c aecclernlkm dtcren.-ws hy one pcn."fflt (ns.•mmc thr rlldhu
{)lanipal ~nm 1'1951
orearth to hef>.ioo km) IKCF.I' •"-II
(a) 32 km (h) 8o l:m
(a) g L< less at the earth's surfoce than at a height nho\'e it
(c) 1.253 bn (d) 6.i bn
or a d,,pth below it
29. The diameters of two plnoets are in the ratio 4 : 1 and
(h) g L< samoat .U plnrei on thesurfareo/the eru1h their me.,n densities in the ratio 1 : 2. The neffier.dion
(c) g has its nuximmn ,'Olue at the equator due to gravity oo the planets will be in ratiollSM Dhuobad • ~
(d) g L< grearer at the poles thnn attheequa!Dr (a) i: 2 (b) 2: 3
22.. Choose the ron-ect s!Jltement from the follo,\ing : (c) 2:, (cl) 4 :t
Weightles:snes.s of an astronaut mO\ing in a satellite is a 30. Al what altitude in metre "'11 the acceleration due to
situation of Larr PMT •9'1sl gra,ity he 2-,"1'6 of that at the earth"s rurface (Radius of
(a) Zero g (h) No gra,ity emth : R mttn-) ( ~ I Dhanbod •99•1

(c) Zero ma"5 (d) free fall (n) l R (b) R

4
 Saptarsbl

(c) }_ R (d) .!!. (c} 1.9l xlO' m (d) 1.0l l( J0 11 m

~ l
39. Whot should be the ,'-'1ocityof earth due to rotntion •bmt
3 1. II the ongular speed of the earth is doubled, the value of Its m,11 ;ms so tlmt the weight at equolor bcromc 3/5 of
oro,lerntion due lo gr,ivily (g) t1I the north pole Initial Y11!11,. R.,dius of e:irth on equator Is 6400 km
If.A)l~-.:r (Med, ) ,.,.,,1 !AMU ,....,J
(o) Do11blc.< (b) 11,:romcs h.11(
(a) 7.-1 •IO " ,-uill , cc (b) o .1 •1U..,,•ml l 1t1.- c
{c) Ren111ins .,,,,. (d) ll«omcs uro
4
At the surfoa, or • rertain plru,et. a<ttla'ation due lo (c) 7Jh to rm/ I "" (d) lt.7 1t, I0 ---1,'t,d l $0!
gimity is one-quarter of lhnt on earth. If a brass boll is
transported to this pLtnet, then which one of the roum,in~ 40. Al what height from the gr<rmd will.lb, value of· g• be the
.'fflmc as I.hat in 10 km deep mine below· the surfucc o(
sb.tcmenls is not romrt (SCRA •9~1 earth
(a) The moss of the brass boll on this pLmel is a quarter [ RPET1999J
of its mass as mearurcd on earth
(n) 20 Am (b) 10 b7,
(b) The weight of lh,, bra.ss bnll on this planel is n qunrtcr
of the wright ns measured on earth (r) 15km (d) 5bn
(e) The brass ball has the snmc 11U1Mon the other plonct An objerl weil!hb 72 N on earth. Its weight nl o height of
aoi on earth 1</2 from nr1h l, IAtms zoool
(d) Th,, bro., b.1JI hM the <nmc "'lunie on the •>llwr (11) J•N (h) 56N
plnnel M on earth (c) 72 N (d) 7-"ro
33. Weight ri I kg ba'Oltlel 1/6 on moon. If radiu, of moon is 111c ruigu]Ar ,..Jocity of Uie earth 1,ilh which it has to
l.7Nl x I 0 6 m , then the mass o( moon \\ill be (Rl'ET 1997)
rotate !i0 that actt.lerntion due to gravity on 60° latitude
becomes uro is (Radius of oarth = 6400 km. Al the poles
(n) l.99 x 10" l:i; (b) 7.56 • 10~ kg g = IOms..!) (EAM CET2000)

(c) 5 .98 x 10" kg (d) 7.65 x 10~ kg (a) 25 x 10 -JnuJfs (b) 5.0x 10 - 1rud"s
34- Rndius of earth is m,und 6000 km. The weight of body al (c) 10 • 1o 'rw11, (d) 7.8 x 10·' 1wl!.,
height of 6000 bn from earth suJfuce beromes
llll'MT 1"7) As>-uming earth lo be n sph,re of• unlfonn density, what
(o) Hair (b) O-f-U. L'I the ,-nJur of gnnitoUonal •~ll'lollkm in a mine 100 km
(c) oncthlrd (cl) l ( o ~ below the earth'• •nrfncc (Clh-cn /! • "400 km)
IAl-°MC "'"'o: Pb, l'MT ..-,J
Ut g bt.• the at.'tt"k-nttit>n due to gravity nl tarth'~ !lurftt~
and K be the mlnlioMI kinetic cn"'K)' of the earth. (3) ~ .t•fHNil~ (b) 1.o<mt., 1
Suppose the e.rth', ndiu., dcm,aes by 2" keeping all
other quantities same.Ihm IBHU ,,..., J IP MER 20001 (c) 5.o6m/ 9 (d) l .10mls 1
(o) g decrea5e5 by 2:'lliand K dem'JIS<S b)· 4'6 If radius of earth is I< then the height ·h' at which vnlue of
(b) g decreasesb)· 4'6and Kincreuesby2'6
'g' becomesone-fourlh is [BHU:>oooJ

(c) g increases by 4" and K ir.:, sos b)· 476 R JR

(a) (b)
(d) g decreasesby4"and Kinmmesby 4'6 4 4
36 . II the radius of lhc earth shrinks by L5'l6 (mass remaining (c) /! (d) R
5'lme), lh<'D the value of accelerution due to gra,ity
dwlge■ by IBIIU ,.,,J •
K 11nd r ""' the rod ii of the e,rth nnd moon rcspcctiwly.
(I) 1'!6 (b) 2'!6 ,,.. and "• arc the dcnsilie of cntth nnd moon
(c) 3% (d) 4'!6 rcspt'dl\'rly. The mtio o( the accclc:.'nltions due to i:ra,i~·
37. If mus of a bod1· is A/ on the earth surface. then U1c """' on the surmct':S o( earth and rnoon is IEAMCf.T 20001
of the same ~ ' on tht moon surfare is
(b) !..&
IAIDl'S t t>'nl RP1dT 1997: JlPME.R 2000) RP.
(a) M/6 (b) Zero
(c) M (d) Nonedthese (c) .!..& (d) !! £..
RP, r P.
38. Moss of moon is 7.34 , 10" kg. II the acrelcrotion due to
46. If the mass of earth is Bo times of thal of a planet and
grn\'ity on the moon is l .-4,,, I s2, the radius of the moon diameter is dooble thot of planet and ·g' on e.irth is
L, Q,M ml., :, t:bm the \'aluc or ·g· on lh:at planet is
IAFMC ,.,.,al
IPl>. l'>ff ' """' Cl') IT 20001
(zt) O,Sb • HJ' ,n (b ) 1.11 -: 1011
m (11) _.,.,,.,,,: (b) o.0Jiln1l1:
 Saptanlhl

(d) !. (c} 1.92 x 10' m (dJ 1.0 1 l( IOMm

l
39. Whol showd be the •~focily of earth due to rainlion •bml
31. tr lhe ongullir SJ-I or lhc earth is doubled, the value or its Ol\ll am so thnl the weight at equator buomc 3/5 of
a<Wleratio:n due lo gr.l\ily (g) t1I lhe north pole lniti:il valut". R.·tdius of earth on equator is 6400 bn
I EA.\ 10.T (Mod.) 1995) I M IU 1999)
(a) Doubles (b) ll<romC5 hnlr
(n) 7.4 11 10 _.Jrur/ l .,ci: (b) o.7J1t lO_..md t 11eC"
(<) l\cmoins """"' (d) llcrom"5 mo
Al the sunaco or • eertain plonct . ...w l..-ntion due lo (c) 7.rc .. ,o ..... nu/! K'C (d) ¥. 7 Jitl0" nu/1 -ux
gm,ity L< Ollc-<Jll.rttr or lhnl on earth. Ir n brn...,. bt1II is
lrdnsportocl to this planl1. Uwn which on• or lh-0 ronm,ing 4 0. At whnt height lram the gound "111U., v•h1e ol'g' be the
snmc A.4 tlu\t in w bn dt~ mine btlo\v tht• surface o(
,tatcmcnL, Is not rom:cl ISCRA ••"'II cn11h
(a) The 1n1U.< o( lhe In<., boll on thl< planet Is " quarter
[IU't:T 199• 1
of it~11lMS as mt.1l5ured on cr.trth
(n) 20km (b) 101:m
(h) 11,e weighIo( f,., bnus hnJI on this plan<! I• 11 quarter
of the •weight n.1 measun..-d on earth (<) 15 bn (d) 5 km
(<) The brass ball lus the some mas.s on the olher plonct 4 1. An object wdghb 72 Non earth. Its \\~ight Dl a height of
rus on earth R/2 from earth is IA,IIIIIS :wool
(d) The brass ball has the same ,-olmne on the oll,er (n) 32 N (b) f,6 N
plnnet ns on enrth (<) 72 N (d) kro
Weight ri I kg bmimes 1/6 on moon. If radiw of moon is 11ie angullir \'elocity of Iii!: earth with which it 1w to
1.768 x I ofl ,,, • Ihm the mass of moon \\ill be (RPET 1997) rotare so that ocreleration due ID gravity on 60• llilitude
beconw m o is (Radius of earth = 6400 km. Al th• poles
(a) 1.99 x 10" -Q; (b) 7.56x 10" kg g =10..,-') [IW\I CFf2000)

(<) 5.98x 10'' -Q; (d) 7.65 x 10 " kg (a) 2.5 x IO .J n:uUs (b) 5.0 x to -:1nuJf:r
34- Radius of earth is around 6000 km. 1beweight or body at (<) 10x101rodl s (d) 7.8 x 10-...2 rud::r
height of 6000 km from enrth sudiice berom6
[RPMT1997l 43- Assunring earth lo be• sphere of• uniform density. what
(a) Half (b) One-fomlh i.s the ,--nlue of gr.nit:itional acceler.ition in a mine 100 bn
(<) One third (d) Kodumg,, below the enrth·s surface (Giwn R = 6400 km)
IAFMC 2000: :Pb, P&IT :aoool
3S- Let g be !be ac<eleration due to gruit)· at earth's surface
and Ii be the rot:Jticm:d kinetic enelg)· of the earth. (a) 9.M m,, ' (b) 7.04 mls 2
suppose the earth·s radius Jeer: m by 2"' keeping al)
(<) 5.o6m/ ? (d) 3. I0 mi., 2
o!her quantities same, then IBHU , _, nnrna 2 0001
(a) g d<'Cn'aSC< h)· 2"' 311d Ii d,m,a,es h)· 4'l6 44. If mdius of earth is R then the bcight ' h' al which ,-alueof
(b) g d,-creases h)· 4'l6 and KincreJIJIS by 2'l6 ·g'becomesone· fourth is [BHU•oool
(cl g lnc._.il50by41hnd /illlQ'IZ!ab)·411> (a) !!. (b) .!!
(d) g d,-m,a,es hr 4"' and Ii i n c - h)· 4'6
ir the nidhos of the earth shrinks by 1.s,t, (mas., remaining
• •
36, (r) R (d) R
some), lht.-n the ,'11111• o( ncaelorntion due lo gnl\il)·
<hinges by IBIIU •- I I(
•
nnd r =the radii of th• earth oncl moon ,..,.,.,.1iwly.
C•l l'N. Chi 2'6 I '.. and ,,. :arc the dcn.silics of caitth nnd moon
Cc) 3'l6 (ti) 4:ir, rc,-pc.'Cth'\'ly. The mtio o( the- 3'.ffll'Tations due to gr.ni ty
3 7. II mass ol • bod,· is M on the .,,.,th surface. then the n>A.« on the surlnce< o( cnrth nnd moon i. 11', \MCt:T 2000I
of the same bodj·on the moon surface is _...._
11 , .
l,UJMS 19'171 RPMT 1"7: J IPl\oU:ll 21>00I (n) (h) ~A
I' , ,.. R I'..
(a) M/6 (b) kro
(<) M (d) ~ne ollhese (<) .!...e.. (dJ !J. .!!.,_
H I', r P.
3 8. Mass of moon is 7 ..14 • 10" kg. If the attelerntion due to
2 4 6. If the nws of enrth is So limes of thnt or n plline! nnd
gr.t\~ty on the- moon i! 1A m I s , the rndius of the moon diameter is dooble that of planet and •g' on earth is
is Q.R mls 1 , then the vnlue of •g' on that planet is
IAFIIIC 199I) !Pb. nrr 199<1; crm 20001
(3) 0 .56 X 10' .. (b) 1.87 • 10 6 m (a) -4.9 ,u/s! (b) 0.9Rn,/s ?

(c) 0 .49 m is' (d) 49 mfs '

 Gravitation

4 7. A man can jump l.o • height of 1,5 111 on• planet .-1. Whal (b) 0-5')6 decrense
i,the hei,ht be may be able to jump oo 11110thcr pland (e) 196 increase (d ) o.$}6 l!'lc,,cn..-.c
whose density il.Dd radius nre, respednT.ly, om,•qunrter Two plane15 of radii in the ratio 2 : 3 are made from the
and one-third thnt of planet A IA-\IU ( Mod.) •oo,J
material of clamtv in th, ratio 3 : 2. Then the ratio of
(a) 1.5 111 (b) 15 m acceleration duo to gra,ity ,:1 / ,:: at the surf.ire of the
(c) 18 m (d) 2am
two plane15 \\ill be [J & K CET 20041
1be acceleration due to gr:nity near the surface of a (a) l (b) 2.25
planet of radius R and deMity d is propartiorusl to
[MPPET2001;AIEEE2004l (c) 4/ 9 (d) O.C?
55. A body weight 500 N on Ille sumce
of the earth- H°"·
(a) 4R- (b) dR ' much would it \\'\'igh half way belo" the surfure of the
earth
(Pb. PET2.001; BHU 2004)
(c) dR (d) d
R (a) 125N (b) 250,V
49. The acceleration due to gra,ity is g at a point distant r (c} SOON (d) lOOO N
from the centre of earth of radius R. If r < R , then 56. Accelerntion due to gra,ity 'g' for a body of mass 'm' on
earth's smfare is proportional to (Radius of earth=R,
[CPMT 200•l mass of e.arth=M) [DCE 2004 I
(a) ,;.-, r (al GM I R 1 (bl ,.•
(c) mAI (d) I R ' 1
(c) g y r· 1
51. The m:wes of two planm are in the ratio 1 : 2- Their
50. A body weight II' ll<"'ion at the surf.ire of the cmth. 115 mdii nre in thr ratio t : 2. Tor at"C'rleration due to gna,ity
weight at , hciJ#,t «1ual to lu1lf th, radil5 of the cmth ,_,11 on lhc plllnds ore in the rntio IMH CET aoo4l
be (D) I : 2 (b) 2 : I
IUPSEAT• ooaJ (c} 3 : 5 (d) 5: 3
w ;:ir Gravitation Polantlal, Enargy and Escape Valodty
(a) (b)
z
.. ,,.
J
,. A bodr of mus m rises to hd11,ht h • R,'5 from the earth's
)(If' ~,ll'foCi', wtw.-rc I( ls earth's rudill$. I( g is nt."t~lcr.it:ion dm:.•
(c) ,, (d)
17 to gra\'ity m earth·$ s11rfi1cc:. tht- incrcn!'ll' In Jl(J(t11tinl
cm.•-rg,r is
5 1, Accclcmlbn due to gmvl~· on moon il< 1/6 of lhc
lCr MT 19 t1q : SCllA 19961 or)rr aoo,I
aoo,lcrntion du, 10 gml'ity nn earth- If lhc rntio of
densities o( earth 1,,_ 1 1md moon Ii',. l is ( ;:: ) •1then (n) mgh

radhtrnf n,oon Rain lemu of l!, .,;nbe IMP PMT • oo3I •

(d) - .,. ,,
1
(a) 2.. R In o gt'll\itationnl field. ot a point whe" the g_rn,~tational
IK '
potenlilll i• rem [CPAIT ·- ·
(c)
.
2. R
'
(d) -!,: R.
~,/ 3

52. The acceleration of • bodv due to the attraction of the

(n) The gra,itntional field is neces>ruily zero
(bl Th• gnnitJ.tionnl field is not DCl't'SS!rily zero
(c) Nothing can be said definitel1· abod the gra\itational
onrtl1 (rndius R) 31 • distanL-., 2 R from the surface of Ille field
earth is (!' = a<tt!emion due to gr.nil)· • t the surfnre of (d) None oflhese
themrth) The gra,itatiooal field due lo a mass distribution is
[ffl'PET2003) 3
£ = K I x in the x-direction. (K isa rolSlant). Taldng lhe
g grmitational potential to be zero 31 infinity, its ,-.Jue at a
(a) - (b) £.
~ 3 distance xis I.MP PET •- I
(a) K/x (b) K/2.<
(c) £ (d) g
4 (c) K l., ' (d) K i :!-,1
\·W ight of a body or mass m decreases by 1'6 when it is The change in potential energy, "i>en a body of mass m is
4-
raised to height h abm-e the earth's surface. If the body is raised lo a heiyit nR from the earth's surf.tee is ( R =
token to a depth h in a mine, change in its weight is Radius of earth) (MP PMT •- I
(KCET2003: MP PMT2003l
 Saptal'lhl

t l. A body of mus m is plnrod on tJMo tarth's surface. u is

<•l mgR -"I 11 -
(b) mngR
taken lrom 1he ..rth's surfaC'O lo • height Ii = 3R . '11le
chaoge in gra\'ilntiooal potentiru energy or the body is
(c)
,,.' (d) mgR - "-
mgR-,- lCBSE PMT:l002)
n· + I n• l
,
•'
5- n,, masses md rndil or the earth llDd moon are ,111. R1 (a) ~ m&R (b) ;;,mgR
and .If,. R: n.-.pffliwly. l11eJr centres are dlsmnre d ·'
apart. Tho minimum ,-elodt\· "ith "tiich a pnrtlcle or mgR (d) !!!Ii!!.
(c)
nlll.<S Ill • ho<1ld h< 1iroJ«11-d rr'om. point midway h<.1W""1l
their centres so that it esrnpcs to infinity i5 IMP PF.T 1997I 12.
2
•
A bod)' of mas m kg. slort.s fhlling tom a point 2R abo\-.
the Earth's smface. Its kinetic """'X'' when it has fallen lo
G
(a) ,, - cM1+.u,, (b)
!G a point ' R. abo\·e the Earth·s surbce [R-R.ldius or F.arth,
" - (M 1 + M~>
d • d . M-Mass of Earth, G-Ora,i tational Constantj[MP PMT 2o,nl
Gm
(c) ' - ( M 1 +,If, ) (d)
(a) .!. G.1/m (b) ! GM••
d • 1 R o R

6. :\ rocket l> inunchcd \\ith velocity 10 km/r.. If r;idius or (c) .: ~ (d) .!.~
earth I• R. then m.ulmum hdghl attained by it will he ~ R J R
13- .~ body L, Jll'OJ<tlOO ve1·llcally up,,-:rtb from the surfoc-< of
( R.PF.T 1991)
a plnnel o( radiu, R ,.;th a ,,,Jocity eq1ml to half tl"'
(>) 2R (b) 3R CS<-.pe ,'!'loci~· for that planet. The maximlllD height
(c) 4R (d) SR altJlined by the body is (l(CE'J' (Engg./lled.J ll002)
(a) R/3 (b) R/ 2
7. lb,re are h,·o bodies or masses 100 kg and 10000 kg
separated by a distance I m. At wha1 distante from the (<) R/ 4 (d) R/ 5
smaller bod)·, the int•n.sity or gra,itationol field will be 14, Ener!l.'· requiml to mo\'e • bod)·of mass m from an Ofbil o(
urn rudiu12R toJR is IAIEf.Ea<HnJ
IRIIU •"71 (n) G,11", U R' (b) G.1/m,J R'
I
(a) -m (b) ..!.. .. (c) CMor•• R (dJ C .1/mlo R
') 10
15- Th• kinetic energy needed to Jll'Ojed • body or nws m
1 (cl) .!2 .. from the earth surfuce (radius R) lo infinity is
(c) - m
11 11 (AJEEE2002.)

8. What is the intensity or gravitational field of the centre or (a) mgR/2 (b) 2 mgR
a spherical shell 1RP~7·,oool (c) mgR (d) mgR/ 4
(b) g 16, R.•lius of otbil ol ••lcllllc of W'lh i5 R. Its kineti< <O"l\)'
LIi JH'O'IX>r1ional l o (IIIIU 20031 Cl'IIT
(c) Zero (d) Noo,olth<s< :&.0041
9. 1be gnl\~tationa.1 potential enCJ~ · of a b:Jcty of mnss • m' at I (b) _ 1
(a) -
the earth's surrur - mgR, . Ills gra,ilatiorutl potentiol R Ii
e11f111Y al a height R, from the earth·s sorfuce will be (c) R (dJ - ,- ,
I
(Elere R, is the radius of the earth) R •
17. In some region. the gmilational li<ld is n,rn. The
fAU MSaooo; MP Pl..Tl.000; J'b. PMT200◄ I
~'T11,1tntional potential in this region I BVP 20031
(b) 1m~R . (a) Mwt be ,wblc (b) Mwt hc l'OIUlnnl
(c) Cannot be um (d) Mu.I he zero
18. A partide&lli towards cmih Imm ininity. ll's veloatr on
reaching lhc "'1r1h would be lOriua JEE 2003)
10 . Escape ,·elocity or a body or I kg mass OD a planet is 100
m/sec. Gr3\1Wional Potential energy o( the body at the (a) Infinity (b) J 2gR
Planet is [MP Pl\lT2ooal
(c) l,/8R (d) Zero
(a) -5000J (b) - 1000J
19. Gas cst"P'5 from the surface ol a planet becaUR it
(c) - 2400J (d) SOOOJ acquires an CM';IJ)C wlocity, The csc:apl' wlocity \\ill
dc11end on "tii<h of the foll•"''UlJI. r..1ors :
I. Mll.«1 of th< pbnct
 Gravitation

IL Mass or the particle escaping (c} m 11 (d) ., .,

Ill. Tempernhll't' of the planet 27. For the moon to cease to remain the earth's sat~ . it3
IV. Radius ortheplanet orbital ,--elocity bas to increase by a factor of [MP P ET 19941
Select the corrttt answer from the rodes gi,i,n below : C•l 2 Cb> E
[SCRA 19<14)
(a) l andll (b) II and IV (c) 11E (d) ./i
28. The escape ,-elocity of an object from the earth depends
(c) I and I\' (d) ~ Ill and IV
upon the mass of the earth (Al). its mean density IP). its
2 0. ,·, and •·,. denotes the escape \'elocily from the earth and
radius (R) and the gravfu11ioool oonsllml (G). Tbns the
another planet h:i,ing !\\ice the rodius and tbe same fonnula for escape ,i,Jocity is (lll' PVT 199,;)
mean density as the earth. Tben [NCEJtT 1,n41 M P Pm •- I
(a) 1·.. : \ ',, (b) I '" : 1·, f l (a) 1· -=
~ (b) P= M
~ 3
(c) r,. -= 2,·I' (d) ,·~ = ,·, , 4
2L Th• escape "'locily or a sphere of mass m from earth
(c} .-:J 2G.\JR fd) ,·=~
R
h»ing mass Mand radius R is giwn by
29. Escape Yl!locity on a planet is v, . If radius of the pL,:net
INCE RT 1981. 84: CBSE P~IT 19'1111
remains same md mass beccxoes 4 times, th, escape
(a) Jl~\f (b) ~ \'elocil)·btcows
1999)
,~, , P'MT 1996: Dl'lIT

(a) • v, (b) 2 ,·.

(c) Jw;'"' (d) JG
;I (r) v,
I
(d) -1 , •
22. The es<ope ,-.,Jocity for• rocket from earth is 11.2 krn/ste.
Its ,-.Jue on a pLm<I where •=lc..-.tion due to gr3Ylty is 3 0 , '111c mru<softhe cnrth is 81 Ii= that oflhe moon and the
double that on the earth and dirun<1,-r of the planet is rndius of thc carth is 3.5 times that of the muon. n"'
r.atio
twice thnt of earth ,.;11 be In krn/...., ISCERT 19831 or the ...._pe ,-.loclty on the surf:n of earth lo that on the
cnn 194Xt; r.1r r 1rr 1000: ursEAT 19991 sutfaee of moon will bcl Mr PIIIT/ P'l.7" 1908: Jll'ill Ell aooo I
(a) 11.2 (bl 5,6 (n) 0.2 Cb) 2.57
(c) 4.81 (d) 0,19
(<) 22.4 (d) 5:).6
23. The es<·;ipe "'locity from thee1111h i..boot II lo11/sl:COlld, 31. n,c cocnpc wlocil)· from the surf:u-. of ellrth is 1:. The
Th• cscnpe \'docit)' from 11 )lWnd ba,i11g twice the radlllS cs,::,pe wloril)· frum the surfac,, of a pl:111<1 who.., nws
and the snmc mean dcnsity u the ""'111, is 1111d mdlus ""' 3 Um,.,. Uu,<c o( lbc earth will be
I NCERT t 910: MP l' ftrT •• 1: Ml' l'fo:1' 2.GOl. (MP PllilT/ P't:t' 1998: J IP P.l t:Jl 2001. mu Pb, l' MT zc,0,41
200'JJ AIIIIIS - " Ul'SUT 1 -I (n) 1: (h) -":
(a) 22 km/.,.. (b) u bn/ u,;
(<) 5-5 km/..., (d) 15,5 kin/,..,
(c) •1:
32, How much "'1<-rx)" "ill he nt:re<.'llll)' for making• body of
24. ,\ ml«ilc L<launched wilh 11 "'lodty less than the """'I'"
500 kg escape from the eorth
velocity. The sum of ii. kinetic ond polffltial "1eri;.;• Is
fMllll 1""6: MP Ph"T 1003I l.i: = IJ.Km s: , radiulo(t'tU'th = O-A " I U"m l
(1) Posim-. IMP p~,- 1- I
(bl Ncgati\'e (11) .~bout • -~• 10• J (b) About • ·• xto' J
(cl 7.ero
(c) About 3. 1>i 10 111 J (d) .-\bout 17.4, 10" J
(d) May be positive or negative depending upon il, inilllll
vdocity 33. The es:eiape ,<elocity (or lhe urtb is 11-2 J:mfs~c. The mus
25- If g is the """"1enitioo due to gmity at the earth's surf""' or another planet is 100 times tb.,t of the earth and ii.
and ,. is the radius of the earth, the esape \'elocily for 11,e radius is~ times thnt of the earth. The escape velocih· for
body to e;cape rut of mrth's gr»itational field is this plnnet \\;JI be I 111P nrr 1999: Pb. PMT 2002)
[Ncritr 1975: RPET 20113) (a) 112.0 km/s (b) 5-6 l-rn/s
(c) 280.0 km/s (d) 56.0 lan/ s
(a) gr (b) .[i; 34, Tbe escape ,-.Jocity of a planet h:i,iog mass 6 times and
(cl g! r radius 2 times :tS that of earth is
(CPMT 19<>9; HP 1'Fr2.003; Pb. PET2002.J
26 . The escape "elocit)' of a particle of mass m ,-aries as
(Cl'YT 1978: RPMT 1999: AIEEE 2002.I (a) '3 •~ (b) 3 1;
(a) .,, (b) m
 Saptllndll

(d) o.pends upon the height from ,.ili,h il is projmed

If ncccll'r.llion due to gm,ity on lbe surfn<'C of n planct is
35- 111c t-'!licnpe ,-.._,focily on cnrth l~ 11.2 J:111/1. On :another lwu ti.mes that on :iurltm: o f e.srth nod it:1 mdlu;s i., doubk
planet hll\ing twice rndiu~ and 8 l-imt.'S mass or the c.1rth. thnt of earth. Then e.«-11pe w locily from the ,mfnce of lh,t
the <SCOl1< \'olocity ,-i1J be IBiloar CMt:ls'I' 109ll pltuwt In onmp.1ri>on lo canh ,.,11 be IRPIITzoo1l
!•l 3,7 km/• (bl 11.2 km/• ('1) 2 V, (b) Jt>
(c) 22.~ km/s (d) 43.:z km/• (c) 4 u. (d) Soncofthesc
36. The ""4.-ape \'Clocil)' o( • bc•I)' on lhe """""' o( lhe earth 'l11i! rArio o( the rndii o( plnnt!ls A and B is i, 1 nncl ral.io o(
ti! 11.2 1-ut/s. If lht carth'.11 mns.1 incrm.'k.~ to Lwicr il•
present valw, nnd lhe rnditL, o( lhe earth becomes half,
liCL-elcmtion due! to g1'11',ity on them ~ k: , ·n,e
ratio of
e.«,.pe ,-docilia from Ihem ,.;JJ be IUIIU 2<10:d
the c<cnpt \'elocily would h<,comc I CBS£ PMT 1997]
C•l 5.6 km/s (n) k 11·, (b) Jt1t,
(b) 11.2 km/ s (remain unchanged)
(cl 22.4 km/s (<) .ff
(d) 44.8 t.m/s mass of 6 'IC w 11 kg is to be~compn-;$ed in a sphere in
37. Gi\'en mass of the moon is 1/ln of the =
of the earth
4Dd corresponding radius is 1/ 4 of lhe eruth. If escape
45. A
such a way tba1 the escape ,-.loci!)· from the sphere is
,-.Jocity oo the earth surface is 11.2 Am/ s, the ,·nine of 3 x 10• mis. Radius of the sphere should be
$IMC on the mrfacc of the moon ~ (G = o.o7 • 10- 11 .Y - m ' fkg 1) (UP-SEA.T auvz)
(CPHT 1997; ARMS 1000: Pb. PMT llOOd (n) 9km (b) 9 m
C•J 0.14 lan/s (bl 0.5 lrm/ s (c) 9 cm (d) 9mm
(c) 2.5 kri/s (d) 5 km/ s TI,e escape ~ of n body on an imogillru)' plonet
38. The angular ,.,lodty of roblllon of star (of moss Mand which is thn<.., the radius of the ear1h and double the
radius R) nl ,-J1ich the mailer stnrt to <S<.!pe from its mus oflhecarthl, (•·, lsthe-,pn-.Jocityofcarth)
"l""lor 11ill be l.\tll en 19991 IMl'al■ CMod, ) 1002.I

(n) Pf (h) J~~I (1)

(<)
J 21J,·.
Ii,....
(h)

(cl) 2
Jl/ 2,.
.Jj,

(<) Pl¥ (d) ./Iff 47. n,c velocity "ilh which n JM'Ojectile DIU'lt be fired .. thol
il esc11pcs earth's gmi~1tlon does not d,pend on
IAIIMS2003I
39- The leosl velocil)• fl"IIDtcd lo U1row • body away from lhe
surfnre of n planet so thnt ii may nol return i., (rndius of (u) Mnss of the enrth
the planet is ti:4 ,. w• m. g =9.8 m/s« 1)1AMO (Enge.) t99'9 (b) Mas,;oftbeprojeclile
(e) Radius of the projectile's orbit
(a) 9 .K x 10..J lflllsa- (b) 12.8 x IOJ m/se£'
(d) Gra,it11ianal constant
(c) 9 .8 x 101 rnh « (d) 11.2,-: 10 1lfJ,~,x-
48. The radios of a planet is .l of earth's radius and ils
40. Escape ,·elocit)· on mrlh ·is h.2 lanfs. IYbot would be the 4
esrnpe vebcity on a ·planet whose Dl3SS is lllOO times and acceleration due to gra,ity is doohle that of earth's
r.,dius is 10 times that of earth [DCEaooi: DPJIIT200~J aCC"eleration d.tJr to grmity. HO\\· many times ";n the
escape ,-elocity nt the planet's surface be as compared to
(a) u2 km/• (b) 11.2 lmfs its ,'lllue on earth's surfuce IBCEC£ 2003: MIi arr 20001
(c) I, 12 l,nf., (d) 3,7 Am/s
41. If lhc racius of a ~nct is R and its dmrlty is p. U,e (a) ""JiI (b) Ii
e,cope velocity from its surface will be IMP PM"r 20011
(a) v, o; fi/ (b) ,·, , {i,R (c) 2/i (cl) 2

fi, I
49. TI1c """'JlC
,-elucit)' for lhc earth is , •. Th< c.«,ipe ,'Clocily
!<l ' · '7 (d) •·, • ...,.,-:: (or u plarK.1 ¥.-hme mdius is four ti~ o.nd dcn~ity is nine
-1,,R tin,., llml of the earth, is IMI' l'bT2003J
42. f.scnpc \'Clod!)' on the cnrth IBIIU aocu I (a) ·' • •·. (b) 12 ,..
(a) h; IC'IJ than that on the 1110011
(<) • •·. (cl) 20 •·.
(b) Depends upon the mas., oflhe bod)•
(<) Depends uponthodi"'Ction ciproitttion
 Gravitation

50. The escope ,'elorlty for a body projected vertirnlly Motion of Satellite
upwards from the surfa~ of earth is 11 hn/s. If the body
is projected al an mgle of 45" "ith the ,-.rtical the escape ,. If .-, and , • represent the escape ,,elocity and orbital
wlocitp,il be I AIEHE2003I \'l'locity of a s:1lellite c:orrcspC11ding to II d rc,~or orbit or
11 mdiu!' R. lhen (CPftrT 19811: MP P)IT
(3) -,;_ ~•mt,, 1-wr.
l(Cf.'r (f.ni:i,./ M«ll 10•"' AIIMS 20021
(<) 22 k111/s (d) 11 bn/ s
(a) •·• = •·.
The acceleration due to gravity on a planet is same as
that on earth and ils radius is four limes that of earth. (b) .Ji,.• = •·.
Whal "ill be Ure ,..Jue of escape wlocity on that planet if
itis ,,,. on earth [RPET 20021 (e) "· = •·• .Ji
(d) ,·. and •·. are not related
(a) •·. (b) ~•·.
a. If r repn....,ts the radius of Uic orbit <A• satellite of 11WS
(d)
,.
.... m moving around n 1dnm::l of ma.°'" M. tht w lodty of tb:
(<) ••·.
2 Mtcllite Is giwn by
A particle or nnss 10 g u, kept on the surf..,. of n unifonn (CPr.rr l9? -U Ml' n n 198 1: Rl'MT 11"9)
sphere of mJISS 100 kg i,nd radius 10 mL Find the work to
(a) ,,-• =,:-
.I/
, (b) ~) -= ~
be done against Ure gnnitational forre between them to r
bile the particle br away from the sphere (you may bile GM
(c) v=- • GM
(d) ,,·=-
G = 6.67 x 10 - 11 Sm: l k,s: l (AIEEE2oos.J
r r
(o) 6.67 , IO""J (h) 6.67 y 10· •• ., Select the corm.-t stntement from the following
(<) 13,34 • IO· •• J (d) 3.JJ • 10-•• J IMl'PMTl9'13l
(1) 111c ,,rt,itnl ,-.locity of • ""tcOitc lncrea.'"'5 \\itl1 thc
53. f"or II t..,tdlltr mrning in nn orbit Mound the cnrth, lbc rodiusofth, orbit
ratio or lclnetic eD"'f.\' to polential en"'f.\' is
(bl Elcape ,-elocity of o 11artick from the surfuce of the
ICBSE PJ,l'hoos) e,11th depends on the speed \\ith which it is fired
(a) 2 (b) (c) The lime period of a salellile does not depend oa the
2 radi115of the orbit
(d) The orbital ,,elodty Ls im-rrsely proportional to the
I
(<) .fi (d) .fi square root of the radius of the orbit
An em1h s;atdlite of mns.s m Tt'\:'01,·~ inn drculnr orbit at
J portlclcs each o( m.., m are kept at ,-.,rticc.< o( an • hdght h from the • 11r1iu·c of the ..rth. I( i• the radius of
«Jllilnlcral triangle o( iddc /., The gmitatkmnl field at the c;i.rth and g i~ :u.'Celcration due to ~ravity al the
centre due t.o Lliesr- partides is I DCE 200-,11 •urfoee or the earth. The \'elocitv of the satellite in the
ol'bit i., giwn by ·
(a) Zero (b) JG.II
INcrJlT 1983; AIEEE 200,d

(a) i:R' (b) gK

(c) 9GM R•h

55. four particles 001 of mnss M, are !orated at the \'Crtlces

L The gmvitationnl potential due to
o( n S<(Ulll'C with side (d) ' R•h
fR'
lhL, at lhcanlll:.of1ho 1q11nrds U,tr11la l'r.l'an11~I Qin.sider a 5'11clllle going m1111d the cnrlh in an orbit.
Which dthe i>tlowing,tnteme1u i, wroog INCFJIT • -I
(a) - ./n~ (b) -& ~
l l" (a) It Lsa freely fulling body
(<) Zero (d) ./n G.1/ (b) It suffers no acreleratioa
L (c} It is IDO\ing with a mnslant speed
There are two planets. The ratio of radius of the two (d) Its nngul,ar momentum remains roostnnt
planet• Ls K but ratio of .acceleration due to grmity of both
plonel!I L, g. \\1,at "ill be the ratio of their <'SCOpe 1•e.lodty 6. Two SllleDites or mnsscs m , and m:tm 1> m: ) are
I.BIIU aoo5J rcvoMng round the enrth In dmd:ir <irblt• or rodlus ,,
(a) l/.i:t' ' (h) tK•1 I : 11nd •!I~ > '! 1 re,rpectlvcl)', \\'hkh of the fa~lo\\ing
(cl tKsi' (d) <K•1 ' statements is true reg.1.rding their speeds 1•1 nnd 1 : ?
(NCERT 19&4; MNR 190,; BHU 19'>8)
 Sapta.....l

(a) Is the same at all poinls in the orbit

(b) Is greatest when it is closest to the earth
(c) ,~, > 1'! (c) Is greatest when it is furthest from the eorth
(d) Goes on increo.sing or decreasing continuously
7- A satellite "irich is geostatio~• in a !"'r1kular orbit is dtpending npon the mass of the satellite
taken to another orbiL Its disb!nre from the centre of 15- The orbital ,-elocit\• of an ortiJiciaJ sarellite in a cirruJa:r
earth in new orbit is 2 times that of the earlier orbiL The orbit just abO\-e the earth's surface is u. For a satl'llite

·-·
time period in the second orbit is (NCEJr:r 1984; M1' PET orbiting .i 311 altitude of hnlf d. the earth's radius, the
orbital velocity is
(a) 4.8 hoa,r, (b) 48.fz hours (MNR•~I

(c) 24 hours (d) :,12 hou,·s (a) -3 ,·

: (b) ./¾·
8. lbe ratio o( the K.E. required to he gn-m to the sntcllite to
,scape eorth's gra,illltionnl field to Uie K.f- requin,d to be
gi\'cn so that Uie ,otcllitc moves in I cimtbr orbit jwl
above cnnil 11tmosphm, is INCERT 1975(
16.
(c)
H. · (d) -l
!
,
In 11 <tlloilite if thc time of l'e\-.lutioo i< 7", then K.F. L<
(a) One (b) l\\ll pro1•111ional to IKHU1993(
(c) Hnlr (d) Infinity
(a) .!. (bl .l.
9. An rutrnn11ul orbit:i~ the enrlh inn dn.-ular orhil 120 km T r'
abo\'e ihe ' " """" ol eorih, gcnily droi,s • spoon out o{
spac-e-ship. 'Ihe spoon \\ill INCERT 10711 (<) .l. (d) r' '
r'
(a) Foll l'erticallyd0\\11 to the eruth If lhe bright d. a satellite from the eorth is neglipllle in
(b) Mo,,, t owards the moon mmporisoo to the radius of U.. earth R, the orbital
(c) Will mm,,along \\ilh spacHhip \le)oc.ityo(the satellite is [IIP PET 1995; RPJrr 2001)

(d) Will mo\'e in an iITegubr way then fall doM1 to earth (a) gR (b) gR/2
10. lbe period of a satellite in a cimdar orbit around a pland (o) ,/g ! R (d) W
is indepenclent of INCERT 197-i; AJ£EE 200,d
18. Choose the cornet statement from the follo"ing : lbe
(a) lbe mass of the planet radius of the orbit of a geosb!tionary sateUite depends
(b) lbe radins of the panel upon
(c) lbe mass of the satellite ( MP PIIIT 1995)

(d) All the th""' parameters (a), (b) and(c) (a) Mass of the satellite, its time period and the
u. II a satellite is orbiting the eorth ,-..y dose to its surface, gmitntional constant
then the orbital ,-.locity mainly depends on ( SCf.Kf 1982) (b) Ma.s, or
the satellite, ma.ss of the eruth and the
(a) The moss aflbe solclll!e only gmilational ronstant
(<) MIL'OI of the earth, mt1s., ri the .,,tcllill•, time period ri
(b) lbc mdius dthe<arth only
the satellite and the gra,i tational ron.<t11nt
(c) lbc orbiW radius only
(d) Mi.s, d. the, earU1, tlm,· pniod of the • t1tcllitc and the
(d) 111• "'""" of th<, earth only gn"itation:al ro!Utnnt
12. 1\m <11tdllk s ,I ond II go l'OUml a pland P in clrcu14r 19. Out or the follm,ing. lhe only inromx1 sll1tcmcnt about
orbit< having nidii 4R nnd R '"-"l"'ctiw~•- II the •1"--.d o( •nlellitd I, lllary•n• CRH 1-I
the -SllteDitc ,I is 31', the spt"<-d of th, satellite B will be.
(a) A satellite cannot 1110\·e in a stable orbit in a plane
fllNR 11)'111 AIIMS 1'11>,1: UJ'SF-A'r 11.000) passing through the eanh's centn,
(a) 12 I' (b) 6 V
(b) eeo.titiorury sotelliles are bunched in the
•
(c) - I'
3
(d) l, i- cqwttorial plane
(c) We can use just one geosbttionary sotellite for globol
13- -~ small s,itellite is re\'Ohing neor earth's surfoo,. Its communication around the globe
orbital ,-elocily "ill be nearly (d) The speed of a sotellite increases with 311 increase in
[CP'MT 1987: 0rissa JEE 200~ JtPllEJt 2001. 02)
the rodins or its orbit
(a) 8km/ s,c (b) 11-2/an/ s,c
20. A satellite is moving around the earth "tth speed ,, in a
(c) 4 km/sec (d) 6 km/sec cirrulor orbit or radius r. If the orbit rodi.ns is decreased
14. A satellite re\'Oh-es :uoum the earth in an elliptical orbit byt%, its speed wil ()IP PEr1996. 99.1002)
[ts speed INCElt.T 1981: t\11' PET 200.J1
 Gravitation

(a) Increase bp'6 (b) lncmise by o.5')6 (I) 11me of m-.,lution of n satrilite just above the cartb's
(c) ll<'Crens, by 1'6 (d) De<-rease by 0.5% surfatt ff., 1
2 1, Orbitn) vclodty of on artificln) !Qtcllilc docs not ck-pend (II) Period o( C1<1<illnrio11 of ma.,s ln,idc the tunnel bon11
upon , .. ,. PMT lff9bl olong the, diru11ct<r olthe earth , r__l
(a) Mns.rnfthe enrth (iii) Period ol simple pendulum h:1'ing n length oqu.al to
{b) Massol lhe5alellite the earth's r.idiu., inn uniform field of 9.8 N/1:,,J 1T. t
(c) Rndiusoflheearth. (i\') Period of an infinite length simple pendulum in the
(d) Acceleration due lo gr.wily enrth's real gra,ititiooal 6eJd CT. I
22- 1be time period of • gl'<l5tationruy satellite is (a) T. , T_ (b) r_ > T.
[IW\ICET 199-4: 1111' PMT 199"1
(c) T~< T,. (d) T.= T- = T.= T•
(a) 24 hours (b) 12 hours
29. \\1tich oflhc foUowlng s!llteU-. is correct In N5p«I o(
(c) :i65 dn)• (cl) One month 1, gt'O.li:tt1lion.1ry -., tcllite. l MP l'MT aoo1I
23. 1\\'0identical 5nlcJlilc.'$ are nt I( and 7R awny (mil\ uiuth (u) II mo,..,, In n plnne <'IMllaining the Cn...,,wich
$Urfnl-e, the ,,imng statement L~ ( R • K.adhL< o( cnr1h) meridian
IRPM'I' 19"71 (b) II fflCJ\-.S in a plane perpendio:ulnr to the rel<stiru
(n) Ratio oftotnl '""XI' will be 4 equotorial plane
(b) Ratio of kinetic energies \\ill be 4
(e} Its height nbo..-e the earth's surface is about the same
astbe radios of the carlh
(c) Ratio ofpotenml energies"ill be 4 (d} ltshcighl abcn-e tbe earth's surface is about six times
(d) Ratio of total energy \\ill be 4 but ratio of potential the ra:lius ofthe earth
and kinetic ene,gies »ill be 2 30. The distlnee of• geo-stationarJ satcllile from lhe centre
24. f or• satellite c:!QP, ,-.,locity is II km/ s. If the sntclllto is of the earth (R.ldius R = 6400 bn) is nearest lo
launched nl an angle of 60' v.ilh the ,-.,rtiral, then <,...I,. IAFMC:00011
Wl0<1ty wfl he ICIISF. PMT t 9"31 l.l'MT 19971
(a) 5R {b) 7 R
(a) 11 km/s {b) .,Jj brt/• (c) IOR (d) 18 R
II 31. If Gr3\itational constant is decreasing in time. \mlll 1,ill
(c) 1j km/s (d) 33lmr/• remain u:nc:hangl.'d in case o( a sattllite orbiting around
e:u1h ( DCE 1999. HOd
25- A boll ls dropped from a spaoernrllft'\'Olving around lhe (•) 11me period (b) Orbiting radius
earth at a height of 120 km. ·wruit "ill happen to lhe boll
(c) Tongential ,-elocily (d) .-\ngulanelocity
[CBSE PM'J' 1996; cnrr2.001; BHU 1999)
32. Given radius of Eruth 'R' and leogth of n day' i the height
(a) II will oootinue to m&,e with wlocity v nlong the of a goostationaiJ satellite is (G-Gravitational Constant.
oriJ;innl omt d sp.11.Wrnft M- Mass of Earth] I MP rMTaoo2.I
(b) 11 will mo,'e "ith the ,nme ,qlffll timg,11tinlly lo the
spm'l."Ctaft (n) ( )"
◄tr~~;.1,
' (b}
(
"•::M) -R
I I

(c) It will !all down lo the e11r1h i;n,d11ally

(d) II will go,,,ry farin the sp.,re
26. An nrtificw satellile is placed into a cirrul:r orbit nround
earth at sud, a h,ight !bat it alwa)~ remains abm'e a
(c) (~.)"4 ,T-
- R (d) t .....
GMT·
--.- r, +R

definite place on tire surface of earth. Its height from the 33. A geo-statiooarysatellite is orbiting lhe earth al a height
surface of enrth is [Al\lU 199"1 of 6 R abm-e the surface of earth. R being the radius of
earth. nie time period of another satellite nt • hcight of
(a) 6400km (b) 4800km
2.5 R from the s11rfoee of earth is
(c) 32000 km (d) 36ooo km (UPSF.AT 2002: JUI U (M ed.>2002; Pb. PET 2003)
27. The weight of an astmnnul, in nn artif-,,,1 sntclllte
~ving around the cnrth. is fBIIU 1999I (11) ,ohr (h) to .f:,1.,
(n) ZCl'O (c) 6 hr (di ~ hr
(b) F..<1111,I lo that on the corlh
(c) More than tlul on lhe eortlt
34.. 11te distance betWt-e.n cen~ o( the eruth and moon is
384000 km. If the moss of the e.irth is • • Io'' kg and
(d) less than that on the earth
28. tn the follm,ing fonr periods (A.VU '1000)
 Sapta,..,I

., ·,.. 11J-.J:: 42. Putcnliul t"IW"S)' of II Slllt.•llite h.1\ing 11ll\~ 'm· and
11
G• 6 ,(lfl x 10 . 111c .speed of the moon is
ncnrly rotaling al a height of c.,◄ x to 6 " ' from the c1111h surf'ncc
(111-1 CET ICHJt] is
(a) 1 i,njsor (b) 4 km/«< IAIIAIS 2000; CBSE PHT 2001; BHU 20o1J

(c) 8 kn1/s« (d) 11-2 bn/ sor (a) -0.Smi;R, (b) -<Ngl,

3S- A satellit, is launched into a circwr orbit of radius ·R' (<) -2,.gR, (d) 4mgR,
around euth while a second satellite is bunched into an
When a satellite goillJ! round the =ti, in • circular orbit
orbit of mdius 1.02 R. The percenmge difference In the
time pc1fods of111e two sntdlltt'S is lf.A)ICET2<10JI or rndius r and speed " looes """"' of it, COeTI!,'', then r
1md u chang~ a,\ IJll'Mt:Jt. 2:0U; EAMClT 10001
(a) 0.7 (bl 1.0 (a) rand v both 1,ith incrca,oe
(c) 1.5 (cl) 3 (b) rand v both 1,ill decrease
36. Distmce of geostationary sotellite from the .mrface of (c) rwi11dttreaseanduwi!linam,r
earth rod.lus{R,, = 6-400 .bu) in terms of R,, is (d) r will dttrease and u will dttrease
44. An earth satellite S has an orbit radius which is 4 times
[Pb. PET2000J
that of a communication sateDite C. The period or
(•l IJ .7• R, (b) 10.10 R, re\'O]utlon of Sis [Ml' P~fT · -OCE 19'1'/I
(<) 6.56 R, (n) 4 di)' (b) 8 di-,;
(d) 2.So R.
(cl 16 do)'I (d) :12 chi\,
3;. l\,'O.!lalcl:itc .<\ and B. ratio of ma.s.,cs 3 : l nrc In dn:ular W11i<h t,eonsmnl for n'°tellit• inorbii
orbit< of rndii r nnd 4r. 11tt'l1 rnlio of total meclu1nbl (Bihar CM£BT 19<1SI
energyof.1 to Bis [DCB•oo•I (a) Velocity (b) .-\ngubr momentum
C•l i: 3 Cbl 3 : i (<) Potmtial ""''ID' (d) Acreler.rtion
(c) 3: 4 (d) 12 : i (e) Kinetic energy
38. The orbital velocity of a planet m ·oMng close to earth's If satellite is shifted tmmrds the earlh. Then time period
surface Is IKPMTaoo2,03l of sntellite ><illbe [Rl'MT:tooal
(a) Increase (b) Dcm,ase
(a) Ji~• (b) .[,; (<) Unchmgl'<I (d) !iothmg cnn be said

(<) J¥ (d) ~
47, 1110 lime period of n , 111cllilo or wth L, 5 /iour,. 1r the
St."']lilration bet\\ttP the earth and thr 511.tellite is increa.""'I
to four times the previous ,'illue, the new time period '"ill
39- U the gra\illllioo>I force between h,,, objects were beconr [AJDIS ,945; AJEEE 2C103J
proportional to 1/ R (:ind not as I / R: ) where R is (a) 20 hours (b) 1ohrurs
(c) 80 hours (d) 40 hours
separation between them, then • partide in circular orbit
uncfer .omrh a fnrn- wo ulrl h:we ib: orhit:al 51lef."l'I u A snlt'Uit', tDO\-es round the earth in n circu]:r oIDil of
proportional to ICBSt: l't-tr ,tQ.. : JtPIUEk 2001. oz) rndius R making one re\'olution per cL,r. A second 5'1tcllite
moving in a circular orbit, m0\"'5 round the cnrth o,,.. in
(al 1/ n' (b) R• 8 dn)'S. Th< 111&115 or the orbil of the "'-'<Ontl s:oldlite is
IUl'SF.AT •oo~J
(c) R' (d) 1/ R
(a) 8 R (b) ~R
40. A satellit, moves around the earth in a dm1lar orbit of (<) 2R (d) R
radius r with speed u. If the mass of the satellite is M , its
49. A per.soo sitting in a chair in a satellite foels weigbUess
total energy is l&lP PMT 2001 I
because [UPSEAT-1
I •
(a) --M,,· (b) -I ~•fl••• (a) The earth does not allrnct the objects in a satellite
2 2 (b) The normlll ron:e by tbe chair on lheperson b;ilana,s
the earth's attrnctlon
(c) -.3: ~(' l (d) Afr" (c) Tho normal force I; 1.cro
(ti) 1'ho penon in .14tdlit• is not 0<ttlrruk-d
4-1. A Mlellile \\itb kin•tk energy £, is m,,Mng round the
earth in a circular orbit. How much more kinetic energy 50. If g y ..!..
1
(instead or ..L •· then t!te relation betw,en
R R'
sboold be J:n""' to it so that il may just escape into outer time period of a satellite near earth's surface and radius R
spncc [Kctrr(CaQ;.fM:t"d.) 2.oot]
><ill be [RPAfT 20021
(a) £ , (b) 2 E,
(a) r' , R' (b) r, a'
(d) 3 £ , (<) r' ,
R (d) r , R
51. To un &'tron.,ul in n ~JJ.11.'t!ShlJ,. the sky apl)enn.
 Gravitation

[KCET 1994) (c) r' ,? (dJ r, ,,

(a) Black (b) White 6. If the earth is 31 on<>-fourtti of its present distance from
(c) Green (d) Blue the sun, the duration of the 1·ear ,-;u be (EAMCIIT •9871
A geostational)· satellite is revohing uwnd the earth. To (a) Half the present year
make It ,scope from gra,itntionnl field of nrth, is wloclty
(b) Qoe-,,ighth the present )Tar
must be irn:rcas("(( (JltK ct-:T aoc,5J
(<) One-fourth the pre.w nt year
(n) l(J(J?r. (b) 41-4'6
(c) 50 % (d) 59.6'6
(d) On,.--<ixth the pr<-,;cnt )'OM
A satellite of mass m is placed at a distnnte r from the 7. The eorth "'"'''"" about Uw, sw, in an <lliptirJtl orbit \\i th
centre or eartti (mass M). The me<hankal energy or the mean radius 9 .3 w I o7 m in a period of 1 year. Assuming
satellite is that there are no outside infiuena,s
(J&K CIIT >OOSI (a) The earth"s kinetic energy remains ronstmt
(a)
GMm (b)
G.\fm (b) The earth"s angulnr momeubnn mnAins ronslant
r r
(cl The earth"•polenHnl """11.''l'l!mains coo.stout
(c)
G'i1/m
~r
(d) -- G,\t,n
~r 8.
(d) .>JI nrorm:t
Vunu, lnob !righter Ihut othor planw bccm1se
I MNR 1'18sl
Kepler's uws of Planetary MoUon
(n) It is hea,;.r th.i n other panels
,. The distance of neptune and satum from sun ore nearly (b) It bas higher density than otherpLmets
10 13 and 10" meters respecti,-el)·. .-\.ssuming that they (c) It i<dOS<'I' totbe earth than otblS' planets
mO\'O in circular orbits. their periodic times "ill be in the (d) II Im no atmosphere
ratio (SCERT 1975: CBSE Pllirr 199.l: MP PET 2001)
9. A planet ttlO\"l"S around the sun. Al a gh·en point P. it is
(a) Im (b) 100 clml'St from the sun nt a distnm."t' ,/1 and has n sp«'d ,., .
(c) 10/io {d) t •J'io Al nnotlk!r point Q, when ii i,; fanh~ t from Uw sun :it a
dlflnnce 1/! . its spt."'Cd will be llil P Pl\rr 1c>K7: IX:lt 1002.I
a. lbe figure shm,'S the motion of a planet around the sun in
an dliptienl o rbit with .sun at the fom.s. 11,r shlldcd IU'CM (bl d,•·1
-~ and B are also shown in the figure which can be J,
assumed to be ,qutl If ,, and , , irpresent the time for
the plane! to m«m? from a lo b and d to c respectively.
(dl
d~,J'.,
then I
(CPIIIT 1986. . .l 10. The orbital speed of.Jupiter i• IMNll 1'186: Ul'SF.AT 2000)
(n) Greater th.in the crhital ,,,,,,dcl earth
(a) ,, < J:
(b) I.es., than lhcorbilnl ']>t<.-d ofr:1rth
(h) '1 ~ ,~ (c) Eqwtl t.o the a-bilnl speed cl earth
(c) '1 = ': (cl) 7.ero
(d) u. Tuu planets IIlO\'e around the sun. The periodic times and
'1 ~ ' :: C
the mean radii of the orbits are 7j . r1 nnd 'i-'!
3. 1hr period of• satcllite in a cimtlar orb~ of r>dius R is T. respecti,-..1)·. The ratio 7j I r, is equal to(CPMT 1978)
the period of another satellite in a cimtlar orbit of radius
4,R is [Cl'IIT1. .a; IIP PET/1'1\TT 1998: 1
(n) l~ l",1 ' (b) 0 I ~
AUMS !ICKH>: cas-.: PM'r 20C>2)
(el •• 1,.,J' (d) t• 'l ~ '
(b) T/ 4
(dl T/8 12. Kepler'• SC<Ond L,w regarding ronst• n,.-y 11r aerial ,-.Jocity
of a pl:mt-t is a c.'OOSCquence o( the law of eonsei,•;,,lion o(
4. Orbit of n planet around a slnr is ICPMT 19821
(CPMT •~o; AIJMS 2002)
(a) Acircle (b) AneDipse
(a) Energ)· (b) .~gnlar momentum
(c) A parabola (d) A stnigbt line
(r) Llnearmomenlum (d) Noneofthese
If a bod)' describes a cimtlar motion under im-.rse square i\ satellite of mass m is rirculnling around the eorth with
field, Uie time lak<n to compk1c ono "'"olulion T is ronsfanl angular wlocity. If radius of the orbit is R., and
rdoted to tht.• radius of the cir\·ul11r orbit .u
m::is~ of the e-llrth M, the nngubr momentum about the
I NCERT 1975: RPM'I' aoooJ
a:ntrcof1hl: -..~rth is IMrnrr 19.,0: Rl'MT1.oool
(a) 7' , , (b) r • ,:
 SaptAl"lhl

(n) mJ GMR11 (b) .11JG.,R,, 23. n,c dirunc,, or • plnnet rrom the sun L, 5 times the
dl<tnn« b<t"""n the ennh nnd the sun. The time period

(<) "'J¥. (d) ..,ff or Uie p!Jinct is

(a) , , ' y,urs
l lll'SF.AT1003I
(b) i ' ' 'I"•"'
(<) i'' y,ars (dl ! ' year., 1

A plnnet iJ m ·oMng nrmnd the sun a" !tiown in elliptic:i

14. n,., "'1r1h £ lllOl'l!S in on cllipticnl omit ,.;th the sun Sat pr,lh LUl'SEAT 20031
H
one or the (od .. SOOMI in figure. Its"""'' or motion will
be maxlnlllltl nl the point IIIIU ' ""4' Cl'MT ,....,, .
C A ·~ ·····+···•·•··•·• C
(a) C • s !
(b) .-1 ,I ·••····i·····•·•· H 'MlC correct OJMion Is IJ
(<) 8 i (11) The lime laken In lm\'elling n\B is le.~, thnn lhot for
(d) D n IICD
The period or mulullon of 1,l11nel ,1 around the sun is 8 (b) 1'hc lim, taken In b·11•-dllnx ll.\ll is gTenltr Uum lhal
times lhnt or B. The dl<tnn,.., or ,I t'rom the , un is how forBCI>
muny time< gr,•ler than thnl or 8 from the sun (c) 11,e lime IAken In tra,,:Ul"l\ Cl>A is le."' thnn that br
ICHSF. nrr ,...,, RIi i/ aoo,J AIIC
(a) 2 (bl 3 (d) The time lllk<'Tl in b·11velling Cl>A is g,"Onlc,• th•n thal
(t) 4 (d) 5 rill' Aile
16. 1r the ri•II•,. o( onnh'• orbit is n••lo 1/~. the durnlion of In lhe pm;ous quetion the orbitol ' "lacily or U1c planet
un ~-nr wilJ bct-ome I BHU 14>q8 : Jll'llf:R 2tJQI, 20 0 2.I will be mlrimnnrnl llll'Sf.AT 10<,:11 RP•:i-. .....1
(n) 8 times (b) 4 limes (n) A (b) B
(<) t/8 lilllC5 (d) 1/ 4 lim.,. (c) C (d) ll
P11.rnclln)' system in the solnr system &..'$:Tib.-s
ux,i; ,_J 116. nw radlu, of orbit or II plom1 b l\\'O tlrn,.. tl,nl of the
eat1.h, The time pcri,xl of planc."l L" ta11u 200:t: Cl'MT2cKJ..tl
(a) Conscf\'lllion or cncrg.y (n) ◄,2 yrors (b) 2.8 !It"'"'
(b) Conscr\'ation o(lint"llr nu111c.ntum
(<) 5.6 yrors (dl 84 Y'"'"'
(t) Cnnsl•f\11lion o( :ani;ulnr mo1nentum
(d) None of these
a7. ·111e orbital nngu!Jir m111ncnl11m or• ;otdllte re,,ihing •I •
distance r lrom the ccnt1'1! is J_ Jfthe distance 15 inc.-wa54.,:l
18. K<-plcr diSCO\ffl.'<I IIIOB auool lo 16r, U,cn th• n,-.,, nngulnr mom•ntum will be
(n) IJm~ or motion I MI' rF.T 1003I
(b) 1,iw. d mlAlional mollr,n (n) 16 I. (h) "-' /.
(<) l.nw, orplan,1ory motion
(d) l,iw. d "'";linear 111,,11011 (<) .!:. (d) ~ L
19, In lhc l!Olor .!)11cm. whith LHOll!Cl'l\•I lllCII 10011 •
28. Acronling to !((pier'• l11w th• lime pcrl<>d or • ,.,dlite
(a) Tot11l El1<~ 0>) K.E. \'llr1CS \\ith its rndalS •• l<>rlu• J•Z 1003 1
(<) Angulur Vdodly (d) Uncar Momentum , I
20, n,., maximum :ond mlnlmum dl"""""" or• comet Imm (n) T' • R (h) r' • 11'
the 51111 nn• K• 10° "' und t ,n • io 1: m. I( it~ velocity (c) r 1 • (IIR 1 I (d) T1 ·•IIIR '1
when na,rc•llolh< sun Is 60 m/•. wh,11 will be It• \'C]odty a9. In plnnctory molion Ute nrcnl w lodty or po,rilion \\~1or of
In m/swben ii I.< farthe:<l lo rl,,a 1 001 I "J>lnnel depend, on 11ng11lar wloc:ity 10,1 and the dl,t.ru,,
<•> 12 (b) 6o or the plan,1 Imm ,mn ( r). tr so the romd relation for
(cl 112 (dl 6 11reul wlacil}'is ll'.AMCt.'1' •0031
2 1. 1\,-o plnnets al aw~n dL<1llml"I! J I J.Od J : from the sun
and their fn"qnrmit~ nru 111nnd n~rcspcrlh"IYthen
.IA
(11) - , .,.. (b) -.IA " rv•r
'
tit Jt
(i.:.,nJa (Mod.I • 0 ..11
JA •
(c) - ., u · (d) :M. , .r;;.
dt Jt
(cl ,, 1,1/ =11:Ji (d) ,,f,1 1 s n f,11 30. K,1,lrr's :«<0nd lnw Onw ol areas) L, nolhlng but a
22. Which d U,c i>II01•ing ••lronm,er finl propo.wd that sun statement of 1u rsr.,,r W"-41
i! stlltlc and c.'llth rounds sun IAt'MC200 1 I (Ii) Woll( didJ!Y lh,'orelll
(•) CoJJCmiru, (b) Kepkr 0>) Con.~11.tion ct lim.-ar mommt11rn
(cl Gnlik'O (d) None