(1) Gravitation is the phenomenon of interaction between

(1) Point masses only

(2) Any arbitrary shaped masses
(3) Planets only
(4) None of these
(2) Force of gravitation between two masses is found to be F in vacuum. If both the masses are dipped in
water at same distance then, new force will be
(1) > F
(2) < F
(3) F
(4) Cannot say
(3) Two point masses m and 4m are separated by a distance d on a line. A third point mass m0 is to be placed
at a point on the line such that the net gravitational force on it is zero. The distance of that point from the
mass m is
(1) d/2
(2) d/4
(3) d/3
(4) d/5
(4) Two point masses m and nm are separated by a distance d on a line. A third point mass m0 is to be placed
@

at a point on the line such that the net gravitational force on it is zero. The distance of that point from the
mass m is
(5) The dimensional formula for gravitational constant:
ab

(1) [L][M][T]
(2)[L]3[M][T]2
hi

(3)[L]3[M]-1[T]-2
(4)[L]3[T]-2
_1

(6) Find net force on one mass due to other two masses

Equilateral
triangle
8

Side L
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(7) Find net force on one mass due to other three masses

Square

Side L

(8) A large number of identical point masses m are placed along x−axis, at x=0,1,2,4,..... The magnitude if
gravitational force on mass at origin (x=0,) will be
(1) Gm2
(2) 4/3 Gm2
(3) 2/3 Gm2
(4) 5/4 Gm2
 (9) Three particles A, B and C each of mass m are lying at the corners of an equilateral triangle of side L. If the
particle A is released, keeping the particles B and C fixed, the magnitude of instantaneous acceleration
of A is
(1) √3Gm2/L2
(2) √2Gm2/L2
(3) √2Gm/L2
(4) √3Gm/L2

(10) Three particles, each of mass m, are kept at the corners of an equilateral triangle of side 'l'. Force
exerted by this system on another particle of mass m placed at the midpoint of any side will be:
1)
5Gm2/L2
2) Gm2/2L2
3) 4Gm/3L2
4) 5Gm/3L2

(11)Find the gravitational force acting between m and the hollow sphere(M,R)
@

(i)
ab
hi

(ii)
_1
8

(iii)
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(12) Find the gravitational force acting between m and the solid sphere(M,R)

(i)

(ii)

(iii)
 (13) A mass is at a distance a from one end of a uniform rod of length l and of mass M. The magnitude of
gravitational force on the mass m due to the rod is

(14)Two particles of equal mass m are moving round a circle of radius r due to their mutual gravitational
interaction . Find time period of each particle.

(15) If distance between two objects decreases by 50% then find the % change in the gravitational force
between the objects.
(1) 200%
(2) 300%
(3) 100%
(4) 400%

(16) If distance between two objects increases by 300% then find the % change in the gravitational force
between the objects.
(17)Two bodies of equal masses are some distance apart. If 20% of mass is transferred from the first body
@

to the second body, then the gravitational force between them

(a) Increases by 4%
(b) Increases by 14%
ab

(c) Decreases by 4%
(d) Decreases by 14%
hi

(18) A mass M is broken into two parts of masses m1 and m2. How are m1 and m2 related so that force of
gravitational attraction between the two parts is maximum?
_1

1) M=2m
2) M=m/2
3) M=3m/2
8

4) M=m
(19)A mass M is split into two parts m0 and M-m0. These two masses are then separated by a distance D.
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If the gravitational force between m the parts is maximum, then the ratio m0/M is
(a) 0.2
(b) 0.4
(c).0.5
(d) 0.6
(20)Two identical sphere are placed in contact with each other. If r is the radius of each sphere, then
gravitational attraction between the two is proportional to
a. r2
b. r4
c. 1/r2
d. 1/r4
(21) Find the distance from 25kg so that the net gravitational force on m0 is zero.

10m
(22) Find net force on m0, placed at the centre of a square, due to other four masses

Square

Side L

(23)Find net force on m0, placed at the centre of a HEXAGON, due to other masses

(24)Three particles, two with masses m and one with mass M , might be arranged in any of the four
configurations shown below. Rank the configurations according to the magnitude of the gravitational
force on M , least to greatest
(1) 1,2,3,4
(2) 2,1,3,4
(3) 2,1,4,3
(4) 2,3,4,1
@

(25) The force between solid sphere (M,R) and m is F, as shown in the figure. If sphere of radius R/2 is
removed concentrically, then find the new force between the remaining part of the sphere and mass
ab

m;
R/2
hi

2R
R
_1
8

(26)A uniform sphere of mass M and radius R exerts a force F on a small mass m situated at a distance of
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2R from the centre O of the sphere. A spherical portion of diameter R is cut from the sphere as shown
in the figure. The force of attraction between the remaining part of the sphere and the mass m will be

(27) Find the point where gravitational field intensity is zero.

r 3M
9M

(28)Find the gravitational field intensity at point P l

P
 (29) Two point masses having mass m and 2m are placed at distance d. The point on the line joining point
masses, where gravitational field intensity is zero will be at distance:
(1) 2d/√3+1 from point mass ′′2m′′
(2) 2d/√3-1 from point mass ′′2m′′
(3) d/1+√2 from point mass ′′m′
(4) d/1-√2 from point mass ′′m′′

(30) Find the correct direction of gravitational field intensity

a. 1
b. 3
c. 4
d. 7
(31)A spherical shell is cut into two pieces along a chord as shown in the figure. P is a point on the plane of the
chord. The gravitational field at P due to the upper part is I1 and that due to the lower part is I2. What is the
relation between them?

(a) I1>I2
(b) I1<I2
(c) I1=I2
(d) No definite relation
@

(32)The force between a hollow sphere and a point mass ‘P’ inside it, as shown in figure is:
(1) Attractive and Constt.
(2) Repulsive and Constt.
ab

(3) Attractive and depends upon the location of P w.r.t centre

(4) Zero
hi

(33) The gravitational force on a body of mass 1.5 kg situated at a point is 45 N. The gravitational field
_1

intensity at that point is

a. 30 N/kg
b. 67.5 N/kg
8

c. 46.5 N/kg
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d. 43.5 N/kg
(34)A large number of identical point masses m are placed along x−axis, at x=0,1,2,4,..... Find gravitational
intensity at origin
(1) Gm
(2) 4/3 Gm
(3) 2/3 Gm
(4) 5/4 Gm

(35) The density of a planet is double that of the earth and the radius of it is 1.5 times that of the earth, if
g is the acceleration due to gravity on the surface of earth then the acceleration due to gravity on the
surface of the planet is
a. 3g/4
b. 3g
c. 4g/3
d. 6g
(36) Two planets have same density but different radii. The acceleration due to gravity would be
a. same on both planets
b. greater on the planet with smaller radius
c. greater on the planet with larger radius
d. depending on the distance of planet from the Sun

(37) Acceleration due to gravity becomes [g/2] at a height equal to

a. 4R b. R/4 c. 2R d. R(√2 -1)

(38) The height at which weight of the body become 1/16 its weight on the surface of earth, is
a. 5R b. 15R c. 3R d. 4R

(39) If the mass of the object is 12kg on the surface of the earth then find the mass of the same object on
the surface of moon
a. 6kg b. 2kg c.12kg d. zero

(40) Density of newly discovered planet is twice that of earth. The acceleration due to gravity at the
surface of the planets is equal to that at the surface of the earth. If the radius of earth is R, then the
radius of the planet would be
@

a. 2R b. R/4 c. 4R d. R/2

(41) If the radius of earth shrinks by 1.5% then the value of gravitational acceleration changes by
ab

a. 2% b. -2% c. 3% d. -3%

(42) If the radius of the earth is R, then the height h above the surface of the earth at which the values of
hi

g becomes one fourth, will be

a. R/8 b. 3R/8 c. 3R/4 d. R/2
_1

(43) The height at which the acceleration due to gravity becomes g/9 (where g = the acceleration due to
gravity on the surface of the earth) in terms of R, the radius of the earth is:
8

a. R/2 b. √2R c. 2R d. R/√2

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(44) Which one of the following plots represents the variation of gravitational field of a particle with
distance r due thin spherical shell of radius R?

a. c. d.
b.

(45)A body weighs 144 N at the surface of earth. When it is taken to a height of h = 3R, where R is radius
of earth, it would weigh
a. 48N b. 36N c. 16N d. 9N

(46) At what depth below the surface of earth, the acceleration due to gravity is same as that at a height of
5km.
a. 1.25km b. 2.5km c. 10km d. 7.5km

(47) Find height where the acceleration due to gravity decreases by 2%

(48) Find height where the acceleration due to gravity decreases by 75%
(49)At what height from the ground will the value of ‘g’ be the same as that in 10km deep mine below the
surface of earth
a. 20km b. 10km c. 15km d. 5km

(50) The moon’s radius is 1/4 that of the earth and its mass is 1/80 times that of the earth. If g represents
the acceleration due to gravity on the surface of the earth, that on the surface of the moon is
a. g/4 b. g/5 c. g/6 d. g/8
(51) Radius of earth is around 6000 km. The weight of body at height of 6000 km from earth surface
becomes
a. Half b. one-fourth c. one-third d. no change

(52) Which of the following statements are true about acceleration due to gravity?
(i) ‘g’ decreases in moving away from the centre if r > R
(ii) ‘g’ decreases in moving away from the centre if r < R
(iii) ‘g’ is zero at the centre of earth
(iv) ‘g’ decreases if earth stops rotation on its axis
a. i,ii b. i,iii c. ii,iii d. I,ii,iv
@

(53) What will happen to the weight of the body at the south pole if the earth stops rotating about its
polar axis?
a. No change
ab

b. Decrease but not zero

c. Reduces to zero
d. Increases
hi

(54) If earth suddenly stop rotating, then the weight of an object of mass m at equator will [w is angular
_1

speed of earth and R is its radius]

a. Increases by mw2R
b. Decreases by mw2R
8

c. No change
d. None of the above
63

(55) How much deep inside the earth (radius R) should a man go, so that his weight becomes one-fourth
of that on earth’s surface?
a. R/4 b. 3R c. 3R/4 d. R/2
(56) Find acceleration due to gravity at a height 32km above the surface of the earth.
(57)The radius of earth is 6400 km and g = 9.8 m/sec2. If the body placed at the equator has to become
weightless the earth should make one complete rotation in:
a. 12 hours b. 1.4 hours c. 6 hours d. 24 hours
(58) At what distance from the centre of the earth, the value of acceleration due to gravity g will be half
that on the surface (R = Radius of earth)
a. 2R b. R c. 1.414 R d. 0.414 R
(59) The value of ‘g’ reduces to half of its value at surface of earth at a height ‘h’, then:
a. h=R b. h=2R c. h= R(√2 -1) d. h= R(√2 -2)
2
(60) At some planet ‘g’ is 1.96 m/sec . If it is safe to jump from a height of 2m on earth, then what should
be corresponding safe height for jumping on that planet:
a. 5m b. 2m c. 10m d. 20m
(61) An object is placed at a distance of R/2 from the centre of earth. Knowing mass is distributed
uniformly, acceleration of that object due to gravity at that point is: (g = acceleration due to gravity
on the surface of earth and R is the radius of earth)
a. g b. 2g c. g/2 d. g/8
(62) Altitude at which acceleration due to gravity decreases by 0.1% approximately: (Radius of earth =
6400 km)
a. 3.2km b. 6.4km c. 2.4km d. 1.6km
(63) When a body is taken from the equator to the poles, its weight
a. Increases
b. Decreases
c. Remains constant
d. Increases at north pole and decreases a south pole
(64) What is the percentage change in the value of ‘g’ on shifting from equator to poles on the earth’s
surface?
a. 4.5% b. 0.343% c.0.05% d.1.5%

(65) When the radius of earth is reduced by 1% without changing the mass, then the acceleration due to
gravity will
a. Increases by 2%
b. Decreases by 1.5%
c. Increases by 1%
d. Decreases by 1%
(66)The depth at which the value of acceleration due to gravity becomes 1/N times the value at the
surface is
@

a. R/n b. R/n2 c. R(n-1)/n d. Rn/(n-1)

(67) Find height where the acceleration due to gravity decreases by 64% of its initial value.
a. R/2 b. R/4 c. 2R/3 d. 3R/2
ab

(68) Find height where the acceleration due to gravity decreases to 64% of its initial value.
a. R/2 b. R/4 c. 2R/3 d. 3R/2
2 2 2
(69) If gravitational potential V=xy + yz + zx , then find gravitational field intensity at (1,1,1).
hi

(70) Calculate the gravitational potential at point P

a.
_1

Square (side L)

P
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b.
L
Equilateral triangle (side L)

(71)Two point masses m and 4m are kept at a distance r, find gravitational potential where the
gravitational field is zero.
(72) If the gravitational potential is taken to be zero at the surface of the solid sphere then find the
gravitational potential at infinity. (Mass = M, Radius = R)
(73) If potential at the surface of earth is assigned zero value, then potential at centre of earth will be
(Mass = M, Radius = R)
(74) Find the potential energy of the system
a. a

b. a a

c. a a a

d. e.
a

e. F
f.

a
@
ab

a
g.
hi
_1

Cude (side a)
8 63

(75) Find the change in potential energy when an object moves from the surface of the earth to height H
above the surface of the earth.
(76) An object is taken to height 2R above the surface of earth, the increase in potential energy if [R is
radius of earth]
a. mgR/2 b. mgR/3 c. 2mgR/3 d. 2mgR
(77) The change in potential energy when a body or mass m is raised to height nR from the earth’s
surface is (R is radius of earth)
a. nmgR b. mgR n2/n2+1 c. mgRn/(n+1) d. mgRn/(n-1)
(78) Find work done in moving 3 point masses from infinity to the corners of an equilateral triangle of side
a.
(79) Four particles A, B, C and D each of mass m are kept at the corners of a square of side L. Now the
particle D is taken to infinity by an external agent keeping the other particles fixed at their respective
position. The work done by the gravitational force acting on the particle D during its movement is
a. 2Gm2/L b. -2Gm2/L c. (2√2 +1) Gm2/√2L d.-(2√2 +1) Gm2/√2L
Square (side L)
(80) Four identical particles of mass m are placed at the corners of a square of side length a, then find the
work required to move fifth mass M from the centre of the square to infinity.
(81) A solid sphere (M,R) and a point mass m are placed at a distance 4R from each other. If the point
mass is released then find the velocity with which the point mass will strike the surface of the solid
surface.
(82) If a tunnel is dug across the diameter of the earth (M,R) as shown in the figure. If the point mass m
kept at point P on the surface of the earth is released in the tunnel, then find its speed at the centre
of the earth.

m
m
m
m
m which has
(83) A stationary object is released from a point P at a distance 3R from the centre of the moon
radius R and mass M. Which of the following gives the speed of the object on hitting themmoon?
a. [2GM/3R]1/2 b. [4GM/3R]1/2 c. [GM/3R]1/2 d. [GM/R]1/2
(84) The total mechanical energy of an object of mass m projected from surface of earth with escape
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speed is
a. Zero b. infinite c. –GMm/2R d. –GMm/3R
(85) The escape velocity of a body from earth is about 11.2 km/s. Assuming the mass and radius of the
ab

earth to be about 81 and 4 times the mass and radius of the moon, the escape velocity in km/s from
the surface of the moon will be
hi

a. 0.54 b. 2.48 c. 11 d. 49.5

(86)If M is mass of a planet and R is its radius then in order to become black hole [c is speed of light]
_1
8

(87) The atmosphere on a planet is possible only if [where v_ is root mean square speed of gas molecules
63

on planet and v, is escape speed on its surface]

a. Vrms=ve b. Vrms>ve c. Vrms ≤ ve d. Vrms<ve
(88) A body of projected vertically upwards with a speed of √GM/R (M is mass and R is radius of earth).
The body will attain a height of
a. R/2 b. 3R/2 c. 5R/4 d. R
(89) A body is throw with a velocity equal to n times the escape velocity (ve). Velocity of the body at a
large distance away will be

(90) If gravitational field intensity is E at distance R/2 outside from the surface of a thin shell of radius R,
the gravitational field intensity at distance R/2 from its centre is
a. Zero b. 2E c. 2E/3 d. 3E/2
(91) A black hole is an object whose gravitational field is so strong that even light cannot escape from it.
To what approximate radius would earth (mass = 5.98 x 1024 kg) have to be compressed to be a black
hole?
a. 10-9m b. 10-6m c. 10-2m d. 100m
(92) The ratio of escape velocity at earth (ve) to the escape velocity at a planet (vp) whose radius and
mean density are twice as that of earth is
a. 1:2 b. 1: √2 c. 1:2√2 d. 1:4
 (93) Two astronauts are floating in gravitational free space after having lost contact with their spaceship.
The two will.
a. keep floating at the same distance between them.
b. will become stationary.
c. move away from each other.
d. move towards each other.
(94) The radius of a planet is twice the radius of earth. Both have almost equal average mass-densities. Vp
and VE are escape velocities of the planet and the earth, respectively, then
a. VP=1.5vE b. VP=2vE c. VE = 3VP d. VE=1.5vP
(95)At what height from the surface of earth the gravitation potential and the value of g are -5.4 x 107 J
kg-1 and 6.0 m/s2 respectively? Take the radius of earth as 6400 km
a. 2000km b. 2600km c. 1600km d. 1400km
(96) If an object is projected vertically upwards with speed, half the escape speed of earth, then the
maximum height attained by it is [R is radius of earth]
a. R/2 b. 2R c. R/3 d. R
(97) A particle of mass ‘m’ is kept at rest at a height 3R from the surface of earth, where ‘R’ is radius of
earth and ‘M’ is mass of earth. The minimum speed with which it should be projected, so that it does
not return back, is (g is acceleration due to gravity on the surface of earth)
a. [2g/R]1/2 b. [gM/4R]1/2 c. [GM/2R]1/2 d. [GM/R]1/2
(98) Let escape velocity of a body kept at surface of a planet is u. If it is projected at a speed of 200%
@

more than the escape speed, then its speed in interstellar space will be
a. u b. √3u c. 2u d. 2√2u
(99) Three particles of masses m,2m and 3m are placed at the corners of an equilateral triangle of side a.
ab

Calculate:

(i) The potential energy of the system

hi

(ii) The work done on the system if the side of the triangle is changed from a to 2a. Assume the potential
energy to be zero when the separation is infinity.
_1

(100) What should be the angular speed with which the earth have to rotate on its axis so that a person on
the equator would weigh 3/5th as much as present?
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(101) A particle is projected vertically up with velocity v = from earth surface. The velocity of
particle at height equal to half of the maximum height reached by it.

(102) The time period of a geostationary satellite is 24 h, at a height 6R ( R is radius of earth) from surface of
earth. The time period of another satellite whose height is 2. 5R from surface will be

(103) According to Kepler, planets move in

a. Circular orbits around the sun

b. Elliptical orbits around the sun with sun at exact centre
c. Straight lines with constant velocity
d. Elliptical orbits around the sun with sun at one of its foci.
(104) The minimum and maximum distances of a planet revolving around sun are r and R. If the minimum
speed of planet on its trajectory is vo , its maximum speed will be

(105) A planet of mass m moves around the sun of mass M in an elliptical orbit. The maximum and minimum
distances of the planet from the sun are r1 and r2 respectively. The time period of the planet is proportional
to

(106) The torque on a planet about the centre of sun is

a. Zero b. positive c. negative d. depends on the mass of the planet

(107) The time period of a satellite in a circular orbit of radius R is T. The period of another satellite in a
circular orbit of radius 4R is
a. 4T b. T/2 c.8T d.T/8

(108) The Kinetic energies of a planet in an elliptical orbit about the Sun, at positions A, B and C are KA, KB
@

and KC , respectively. AC is the major axis and SB is perpendicular to AC at the position of the sun S as shown
in the figure. Then
ab

a. KA < KB <KC
b. KA > K B > KC
c. KB>KA > KC
hi

d. KB <KA <KC

(109) The figure shows elliptical orbit of a planet m about the sun S. The shaded area SCD is twice the shaded
_1

area SAB. If t1, is the time for the planet to move from C to D and t2, is the time to move from A to B then

a. t1= 4t2 b. t1=2t2 c. t1= t2 d. t1> t2

8 63

(110) A satellite A of mass m is at a distance of r from the centre of the earth. Another satellite B of mass 2m
is at a distance of 2r from the earth’s centre. Their time periods are in the ratio of

a. 1:2 b. 1:16 c. 1:32 d. 1: 2√2

(111) If a satellite of mass 400 kg revolves around the earth in an orbit with speed 200 m/s then its potential
energy is

a. -1.2MJ b. -8.0MJ c. -16MJ d. -2.4MJ

(112) An artificial satellite revolves around a planet for which gravitational force (F) varies with distance r
from its centre as F ∝ r2. If v, its orbital speed, then
(113) Assume that the force of gravitation F ∝ 1/rn show that the orbital speed in a circular orbit of radius r
is proportional 1/ r(n-1)/2 to while its time period 2 ( T is proportional to r(n+1)/2,

(114) Two particles of equal mass m are moving round a circle of radius r due to their mutual gravitational
interaction. Find the time period of each particle.

(115) Two satellites 4 and B go round the planet P in circular orbits having radii 4R and R respectively If the
speed of the satellite A is 3v, the speed of satellite B will be

a. 12v b. 6v c.4v/3 d. 3v/2

(116) When energy of a satellite-planet system is positive then satellite will

a. Move around planet in circular orbit

b. Move around planet in elliptical orbit
c. Escape out with minimum speed
d. Escape out with speed greater than escape velocity

(117) An object is projected horizontally with speed , from a point at height 3R [where R is radius
and M is mass of earth, then object will]

a. Fall back on surface of earth by following parabolic path

@

b. Fall back on surface of earth by following hyperbolic path

c. Start rotating around earth in a circular orbit
d. Escape from gravitational field of earth
ab
hi

(118) The orbital speed of a satellite revolving around a planet in a circular orbit is Vo . If its speed is
increased by 10%, then
_1

a. It will escape from its orbit

b. It will start rotating in an elliptical orbit
c. It will start rotating in an elliptical orbit
8

d. It will move in a circular orbit of radius 20% more than radius of initial orbit
63

(119) When speed of a satellite is increased by x percentage, it will escape from its orbit, where the value of
x is

a. 11.2% b. 41.4% c. 27.5% d. 34.4%

(120) In an orbit if the time of revolution of a satellite is T, then PE is proportional to

(121) If potential energy of a satellite is -2MJ, then the binding energy of satellite is

a. 1MJ b. 8MJ c. 2MJ d. 4MJ

(122) The time period of polar satellite is about

a. 24hr b. 100min c. 84.6 min d. 6hr

(123) When energy of a satellite-planet system is positive then satellite will

a. Move around planet in circular orbit

b. Move around planet in elliptical orbit
c. Escape out with minimum speed
d. Escape out with speed greater than escape velocity

(124) A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very small
compared to the mass of the earth. Then

a. The acceleration of S is always directed towards the centre of the earth

b. The angular momentum of S about the centre of the earth changes in direction, but its magnitude
remains constant
c. The total mechanical energy of S varies periodically with time
d. The linear momentum of S remains constant in magnitude

(125) If L is the angular momentum of a satellite revolving around earth is a circular orbit of radius r with
speed v, then

a. L∝v b. L∝r c. L∝√v d. L∝√r

(126) If acceleration due to gravity at distance d[< R] from the centre of earth is B, then its value at distance
d above the surface of earth will be [where R is radius of earth]
@
ab
hi

(127) If the gravitational force between two objects were proportional to 1/R (and not as 1/R2), where R is
_1

the distance between them, then a particle in a circular path (under such a force) would have its orbital
speed v, proportional to

a. R b. R0 c. 1/R d. 2R
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(128) Calculate the energy required to put a satellite of mass (m) from earth surface into an orbit of radius,
4RE, where RE is radius of earth.

(129) If an artificial satellite is moving in a circular orbit around earth with speed equal to one fourth
of ve from earth, then height of the satellite above the surface of the earth is

a. 3R b. 5R c. 7R d. 8R

(130) If potential energy of a body of mass m on the surface of earth is taken as zero then its potential
energy at height h above the surface of earth is [R is radius of earth and M is mass of earth]

(131) A small satellite is revolving near earth’s surface. Its orbital velocity will be nearly

a. 8km/s b. 4km/s c.11.2km/s d.6km/s

(132) Two satellites of mass m and 2m are revolving in two circular orbits of radii r and 2r around an
imaginary planet, on the surface of with gravitational force is inversely proportional to distance from its
centre. The ratio of orbital speed of satellites is

a. 1:2 b. 1:1 c. 2:1 d. 1: √2

(133) The addition kinetic energy to be provided to a satellite of mass m revolving around a planet of mass
M, at transfer it from a circular orbit of radius R1 to another of radius R2 (R2 > R1) is

(134) Two satellites of earth S1 and S2 are moving in the same orbit. The mass of S1is four times the mass of
S2. Which one of the following statements is true?

a. The potential energies of earth and satellite in the two cases are equal
b. S1 and S2 are moving with the same speed
c. The kinetic energies of the two satellites are equal
d. The time period of S1 is four times that of S2

(135) Four particles of equal mass are moving round a circle of radius r due to their mutual gravitational
attraction. Find the angular velocity of each particle.
@

(136) A small object projected with speed vo of mass m then find minimum value of vo so that it can reach
the surface of another planet as shown in the figure
ab

12R
hi

Planet A Planet B
(M,R) (4M,2R)
_1
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