6. 4.

JEE-Physics
(A) toTwo (D) E)(B) (A) Mark The (3/4)(A) mass axis?
! m,1sThe whichmoment
lengthas )
of A(AAC Figure throughcube;
objects,
Eight
point
each point 4Ma(A)
MR'5 concentric Axis Axis Axis Axis square distance
other the is each
DD', CC, B, A, parallel
of mass
shows
CORRECT one
passing structure inertia side
as passing pasSing of shown m, a edge
shownringsalong the to rectangular
1s is
through shown
each of
connected of of
each the through centre
in through option (2/3)(B) ( the the in the each
length
(BMR
), of
figure.diagonal other AB} HF 6Ma?(B) cube?
3 in
system
figure. of
radius one the of
regardingfigure and wire a.
mass
mass to What
D
two of
The Rof centre
the perpendicular about It a ABCD. M,
and adjacent
the m consists of point
is
moment of observed is
point the the D the are
mass
structure the
the mass The
point
masses page) to
A(normal moment of system two moment theat
of M structure
four to axes that m, (CEG vertices
(C)MR' inertia are I, (1/2)(C) ) moment 8Ma?(©
joined masses from the by
= and point
of the of
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B(normal inertia rod BB a
of normal massless B of inertia of
together
the Inormal masses the is and ratio
= inertia a
system 2ma² of point AA, of massless
rigid,
of
to the =3. the rod this
such the to connected of
and structure the arrangement
MR?
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plane (1/4)(D(
their (DAD
) wire10Ma?(D)
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structure = mA minimum
A about
AA' ma the of
are negligible
perpendicular
is following
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: I, about axis the
B B
= form
3ma", mg
axes: masS. which passing
ALLEN
ofa

10 9 8.

(D) (C) (B) (A) pieces 270(A) While (A) 2The

Abody kinetic no A Moment A ALLEN
(A)I, 1,
+ moment theIn
woman friction. 60kg disc
is has shown
Columnl initially
shown energy the woman of of
woman
walks The inertiaradius
mr inertia
(in figure
in
moving raftstands
J) to of R, of
columnl walkS,
of is
the disc mass this half
180(B) the (B1.)5front 0.5 on
towards system she (B),mR? about mR*m(B) system of
and 60kg mthe 5 and the
maintains of 6m from back
Paragraph
possible the z-axis has about part
right(woman 120kg
raft a of is
fixed a moment
explodes a and 6m passing the disc
(S) (R) (Q) (P) plus 0.5m (disc
ring
mass constant pier, long, for shown and
3 stops.
ratio raft) (0.C5) Question
as 3mR2(C) through of other
into 210(C) inertia Smp?(C) axis
Impossible <m, m, m,
= ane speed How Figure.
shown120kg
in 3
m,
>
Columnll two 2
shown OI,, ishalf
of far(in raft 8 :
pieces and will I, is
3 that a
in m) ms 9 be: I, ring
for column l is is and
any and2. relative the floating both
I,
masses 330(D) (D)
2.5 raft about (D)
lI of
Direction to from at mr mass
the rest axis 4

raft. the as m
in ROTATIONAL
MOTION
of pier shown and
Find still
motion now? water radius
the in
of total figure. r.
the with Then
 ROTATIONAL MOTION
JEE-Physics ALLEN ALLEN
Find its moment
M. Two identical hollow spheres of mass Mand radius Rare joined together, and the combination is rotated midpoint to form anL shaped rod as shown.
16. Arod of mass 4kg & length 4m is bent at
about an axis tangent to one sphere and perpendicular to the line connecting them. The rotational inertia of inertia about the point O.
of the combination is

10 40

(A) kg-m²
16
(B) kg-m? (okg-m (D)kg-m
32 34
(A) 10 MR? (B) ; MR (C)MR MR'
17. Consider a rod AB of length L whose
mass per length is given by 2 =(1+ Kr) where K is a constant
and
moment of inertiaof the rod will be least about an axis passing
Auniform square plate S (of side c) and a uniform rectangular plate R (of sides a&b) (a >b) have xis the distance from the left end A. If the
identical areas and masses. Given (a) I,<l; (b) I,1; (c) LAlwhich of the following is through point P. Then AP is equal to :
CORRECT: 3L + KL) 3L + 2KL'
(3L + 2KL' 2L + 3KL
(D)
(A)|6+ 3KL (B) 6+2KL
(C)4+3KL
mass M each. They are placed on (5,0,0), (0,5,0)
4+ 3KL
and (0,0,5).
A system consists of three point masses of
b
18.
inertia are 1,, I, and 1, respectively.
When it rotates about x-axis, y-axis and z-axis, the moment of
Choose the correct alternative/s:
(A) I, +I,=1, (B)I +I,=21, (C) ,=1,=I, (D) I,-I,=1,
R each. The frame is placed in x-y plane
(D) None 19. There is a square frame ABCD of 4 rods of mass m and length L
(A) a, b (B) b, c (C) a, b, c is perpendicular to xy-plane through M.
as shown. AC is a line in x-y plane that is taken as w-axis. z-axis
3. Three identical rods,each of length l, are joined to form a rigid equilateral triangle. Its radius of x,y, z, w axes repsectively.
M is mid point of AD. I,I, I, I are moments of inertia about
gyration about an axis passing through a corner and perpendicular to the plane of the triangle is

(A)C (B) 5 (); (D)

D

The momentof inertiaof a uniform flat disc about the axis passing through centre and perpendicular to
the plane of disc is I. The radius of the disc is "a". A quadrant of the disc iscut off and is replaced by a
material having twice the density of material of disc. The moment of inertia of the new disc about the
B

same axis will be: List-II

List-I
31 31 SML
(B) 8 (D) I (1)
(A) (P) 3
4
through
Moment of inertia of a square uníform lamina about an axis perpendicular to lamina and passing (2)
10ML
passing
centre is I. Moment of inertia of this lamina about an axis perpendicular to plane of lamina and (Q 3

through a point P is 21. Locus of such points is a : 7ML

(3)
(R) 3

2ML
(S) (4) 3
Codes :
P R
4 3 2
(A)
3 4
(B)
4 3 4
(C)
(B) Straight line (D)
(A)Square point P.
(D)There will be no such point other than
(C)Circle
 ROTATIONAL MOTION
JEE-Physiks ALLEN ALLEN
the other pan of a false
24 gms when placed on
20, Square frame is made of four uniform rods. Mass of each rod is m and length . when placed in one pan and of the body is :
Column 24. Abodyweighs 6 gms when both the pans are empty, the true weight
Column-II balance. If the beam is horizontal
(Axis of rotation) (Moment of inertia) (B) 12 gm
(about axis of rotation) (A) 13 gm
(D) 15 gm
/
(C) 15.5 gm natural lengths are 2/. and
is cut into two parts so that their
An elastic string of natural
length 3/,
distance between P and Q being 7, and the
25 P and Qthe vertical
(A) (P respectively. They are attached to points equilibrium supported by the string at
3 uniform rod CD=40cm is in
horizontal distance being 12cm. A of the parts CA and BD in cms
are
horizontal then the lengths
t A and B.If the rod CD is
(B) ()
PO
J2cm
DD
A B
7
(C)
(R) m (B) 14,14 (C) 16,12 (D) 10, 18
(A) 12,16
smooth vertical wall and rough horizontal floor as shown. A boy starts
Aladder AB is supported by a INCORRECT statenment :
26. renains at rest, then pick up the
(D) 8
me?
moving from A to B slowly. The ladder
(S)

21. Three identical rods are hinged at point A as shown. The angle made by rod AB with 1B
vertical is
Smooth
Wall

B 90°
Rough floor
90
increase.
C (A) Magnitude of normal reaction by wall on ladder at point B will
Ay tan (B) tan
&) (C) tan-(1) (D) tan (B) Magnitude of normal reaction by wall on ladder at point B willdecrease.

(C) Magnitude of normal reaction by floor on ladder at point A will remain unchanged
22. Two persons of equal height are carrying a long uniform wooden
beam of length /. They are at distance
l14 and /6 from nearest end of the rod. The ratio of normal reaction at their heads is
(D) Magnitude of friction force by floor on ladder at point A will increase
is the horizontal force exerted
27 A semi circular wire of mass m is hinged at its top on a vertical wall. What
by the wall on the lower end.
A) 2:3 (B) 1:3 (C) 4:3 (D) 1:2
A uniform ladder of length L rests against a smooth frictionless
wall. The floor is rough and the coefficient
of static friction between the floor and ladder is u. When the
ladder is positioned at angle 0, as shown in
the accompanying diagram, it is just about to slip. What is 0 ?

mg
(A) mg (B)

(CY 2mg (D)

3mg
(A)cos 0=u (B)tan = 2u (C) tan 0= (D) sin 0=
6
 JEE-Physics
Figure
showsZ8.
(D) (C) (B) (A) Codes : (S) (R) () (P) case
2 2 2 2 calculate
Axis
Axis Axis Axis List-I
passing passing passing passing particles
cach
moment
1 3 4 through radiusof
through through through
edge edge of
inertia
the edge symmetry length length connected
cylinder L
= edge centre
centroid
R of of
tetrahedron of of of assembly
cube cube of
axis upper cube rigidly
of
8 base ofcylinder = =
L and L
3 4 4 3
about by
=
L lower nassless
axis
faces shown
thin
rods.
in
(4) (3) figure.
(2) mL?(1) 8
Mass
mL? 3
m2 4 List-II
mL? of
each
particle

is
m.
InALLEM
each

30.
31.
(D) (C) (B) (A) mb InALLEN
(A) 2 lbe Two
M/wimwhich lamina axis edge A
symmetric
Column-II
uniforn through of 2mb Column-HColumn-I
is about 4 mb mb3² 3
the
then Shows
square Shows
pivoted rods the its lamina
tangentcentre as rigid
of of the
about equal mass
offig.in bodies
moment
(B) 3 ABmass
O
length in The M
as the and consists rotating of
shown. side
but plane
perpendicular of (P) inertia's
(T) (S) (R) (Q) about
different
If the of
of Column-Il
in lamina issquaresquare square.
a of
it.
maximum Adiagonalits Four
having b
about Three andabout bTwo
vertical itat of
equilibriunm ring form form s rod A certain
certain
(C)V2 Which rods passing rods one of
masses to is of the an rods axis an
30 length rotating endlength
the 2a.shape mass each equilateral
median each each
L
axis. rigid
issize perpendicular
through shaped
the are
plane The with
rotating of m of of of about making
2b
rigidly of of
body.
body moment
is diagonal mass mass and
a squarewhich the mass
1.6Ma.
semicircular triangle junctionstructure verticalangle
m mass
is m triangle
joined about ofcan m to and
in of side form
b, and
(D) V3 the Theinertia accommodate rotates plane
of
30° m
and rotatinglength axis. fixed
shown to diagonal 2b length two of with
form moment section inside square a rotate
of about rods. L ROTATIONAL
MOTION
an the
configuration, lamina
L-shaped of over
inertia
each
about
of of
ratio body
the anthe
 JEELis ROTATIONAL MOTION
32 ALLEN
Assamng frictionisscontacts. the magnitude of extermai order for
meter Stick that has the same mass as therock. In
cquilibium of the rod (The rod is uniform and its mass ishorizontal forcePapplied at the lower end for e
'm) is cqual to A rock isatached to the left end of auniform
the triangular object in figure. how far from the
balance on
the combination of rock and meter stick to
left end of the stick should the triangular object be placed?
Rock. ass m Meter stick. mas m

mg (B)0.25 m
(A) (A) Less than 0.25 m
2 (B)cos (C) tan mg
(D)cot 0 (D) 0.50m
33. (C) between 0.25 m and 0.50 m
Three plates of same thickness (neglegible) and made of
coTect opion : same material are kept as shown. Choose the 37. System is in equilibrium. Find the hinge force (N)
A
A

20kg

Sm

b
(A)All must have same mass and moment of
(B) All must have same mass and
inertia about A, A,
different moment of 400
(C)All may have same mass and may have different inertia aboutA,A, (A) 1000 N (B) N (C), (D) None
D)all will have different mass and moment of inertia about A, A,
On a disc of radius R a
different moment of inertia. 38. In the figure shown a uniform rod of mass m and length (is hinged at one end & other end is connected
concentric circle of radius R/2 is drawn. The disc is free to rotate to a light vertical spring of spring constant k as shown in figure. The spring has extension such that rod
fricionless axis through its centre and perpendicular to plane of the disc. All about a
the disc) shown in figure are act the three forces (in plane of is in equilibrium when it is horizontal. The rod can rotate about horizontal axis passing through end B.
tangentialy to their
the net torque (about centre of disc) acting on the discrespective circular periphering. The magnitude of Neglecting friction at the hinge find force on the rod due to hinge.
is :

279

2F

(A) 19 FR (B) 2.3 FR (C) 2.5 FR (D) 1.5 FR mg mg

35. Three identical uniform rods are hinged on a wall. (A) mg (B) (C) (D) "3
while their other ends are attached to a wall by 4 2
massless strings as shown inthe diagrams: three
39. Two identicalrods each of mass mand length are hìnged at one end at P.A forre Fis applied at one
end of vertical rod as shown in figure, system is in cquilibium. Then fore applied by the hinge is :

20
9)
(1)6 (i1)

(A)Tensionsin strings (ii)and (i) are same (B)Tensions in strings (i) mg

(C)Tensions in all the srings are same and(ii) are same (A) (B) -mgi mgi (C) i.2mgj (D) -mgi 2mgg
(D) Tensions are
different in all the strings
 43.
42.
R,(A<) 41. 40.
hinges JEE-Physics
R
vertical in A(D) (C) (B) (A) is
vertical (C)
rectangular The The The The corect As (D) (B) (A) wooden denser the Figures (C) (A)
on
shown 0'The Ois greater The
The greater figure).
(see is A
The steel The The tied
pulling
pulling
pulling upward issmaller man
thplane
e line pulling
) till smaller angular angular angular angular
in end. end. than normal tension
1 to
metal the the than than and the of
(with metalforceforceforceforce rodforce [Neglect wood.) In
figure,
acceleration than
thanacceleration the the 2 floor mass85
plate plate acceleration
acceleration figure below reaction in
decreases,
increases, is is becomes
*N
(B) F the the torque torque In cable stands
by kgon
eunchanged,
is unchanged, lifts arotational Gravity] figure 2, a
R AB uniform
rotational
best, ABCD the show at is steel
up about about WOOd
vertical) horizontal support 1000
depicted
P 4 isits itS the wil will will will Figure 1 stick 1, a cable,andthe
supported rod rod be be O. O'. thmeter
e Cable
N one
moment its
momentof its inertia inertia be be is
moment greater greater steel pivoted stick is
as moment slowly can greater greater stick, 3700 end of
by
shown ? 0.5m
of be about
aboutO. is
12 by rotated for for pivoted board
(C) forceforce of of from for for
at half N a
intwo the 0the the uniform
he decreases.forceforce
tdecreases. positionfreely stick stick the the steel of(D) (B) 2im - is
figure.hinges stick WOod
which
at The supported
increases.
decreases. stick end, the The board
in in
P, shown,about figure figure in inFigure 2 wooden normal tension
The and at is of
figure figure O, wood Mass
steel fromlength 2
contact P, point 2 1 and end,reaction in
so which becausebecause 2, and cable
(D) that A an belowjust
because because 1, at half
forces of in identical O, m
it the the at is and
remains the the and support of2700N
A rotational
rotational
R, vertical
following the which 0.5 mass
the
and torque torque
forceforce a
m
in is from
caklthe 15
, k, plane. is 1700N is kg.
equilibrium statementS inertia inertia applied Fis steel.
exerted about about The
When applied
about about (Steel other
by 0 O to ALLEn
a is is the to i end4.

47. 46 45
ALLEM
(D) (C) (B) F=mg/2A
(A) angleThereshown. (A) respectively.
Thenfloor,
: ?xY=0 (t the
One (A) Select (A) (Rodabout A
massless = uniform
The The The
cquilibriummg
is The end torque, is A
betweenexists as
magnitucde magnitude A of rotating in
minimum minimunn light shown option : vertical rod
a incorrect
v=
no spool stick
two
inextensible
friction in velocity,
of clockwise)plane. massof
value value of surfaces
of figure. with
inner
force force mass (B) m
at (B<F
) F, 0=
of' ofA point radius Let
Whichlength
:
u on on isthread mv.O
for lor 0. F,and
angular of
the the A, r, =
the the is and 0 the is(
spool spool whiletightlyouter length
systenn system F, velocity, followinghinged
at at the radius F, be l
to B tan 0 B wound the is Hinged A at
to in coefficient
in Pivot pivoted A.
13remain remain vertical (C) a represents
order order =FRR = It
around (C)Fis is
placed angular
o
in in to to on >x released
cquilibrium
uilibrium maintain maintain of forces a a the
the
friction against wall =0
acceleration, hinge from
spool onand
cquilibriunm between vertical force the
through the the
is is leftother
(R/r)-l (R/r)-1 (D) (D) whengiven
tan
çv=0 (D) a,
cot 0 spoolwhich wall and
F end =
is right centripetal
position
rod
and =
and a F, rests ROTATIONAL
MOTION
masstilted becomes
= ends so
point mg on
m
split acceleration)
of a that
B is cos frictionless horizontal.
hanging.
is the it
u. floor as stick, rotates
The
 ROTATIONAL MOTION
JEE-Physiks ALLEN
ALLE shown with a
angle 30 with horizontal as
kept in equilibrium making
Paragraph for question nos. 48 to 50 53 Auniform rod of mass m is
A sold cyl1nder of mass m is kept in balance on a fixed incline of angle a= 37° with the help of a thread thread. The tension in the thread is
fastencd to its jacket. The cylinder does not slip.

(D)data insufficient
mg (C) mg
(A) (B) mg 2 . Rod is hinged
2
are attached at end points of a massless rod ABof length
48. What force F is required to keep the cylinder in balance when the thread is held vertically ? 54. Twoparticles cach of mass m
horizontal position. Athe instant when rod reaches
released from rest from
at point Cas shown. Rod is is/are CORRECT:
mg 3mg Smg of the following
(A)
2
(B) 4 (C) (D) None of these its vertical position as shown, which m

49. Inwhat direction should the thread be pulled to minimise the force required to
hold the cylinder ? What
is the magnitude of this force ? m
3U4 m

(A) parallel to incline (B)venical mg

10

mg
(C) horizontal (D) None of these
5
at A
(A)Speed of the particle at B is thrice the speed of particle
50. The values of minimum cocfficient of static friction between cylinder and incline in the cases mentioned
in above two questions are and respectively : 6mg
(B) Net force on particle B is
4 3 4 3 3 3 (C) Angular accelration of the system is zero
(A)77 (B) (C) (D) None of these
48 (D) Both x & y components of hinge force are nonzero
Its foot does not slip on the ground.
51. Acone of radius r and height hrests on a rough horizontal surface, the coefficient of friction between the 55 Auniform rod kept verticallyon the rough ground falls from rest.
conc and the surface bcing . Agradually increasing horizontal force Fis applied to the vertex of the Then:
cone. The largest value of u for which the cone willslide before it topples is (A) no part of the rod can have acceleration greater than g in any position
(B) at any position of the rod, different points on it have different accelerations
(C) any point on the rod has different accelerations at different positions of the rod
(D) the maximum tangential acceleration of any point on the rod, at any position, is 1.5g
Paragraph for Question 56 to 58
position from rest. When it
2r A rod of length ( and mass m is hinged at A. It is released from horizontal
(A) =2h (B) = Sh (C) u= h (D) | = comes to position AB, and makes and angle of 30° with vertical
52 A uniform ladder of length 5m is placed against the wall as shown in the figure. If coefficient of friction
uis the same for both the walls. what is the mininmum value of u for it not to slip?

5m
4m 56. Then the angular velocity in this position is :
3m y1/2 o-l2
(B) (39" (c)() 4/
(A) u= 1/2 (B) | = 1/4 (C)u= 1/3 (D) =I/5
4
 ROTATIONAL MOTION
RE-hysis ALLEN ALLE
$7. the centre of a disc of same
C piscd by thc hingc on the rod along thc rod
is; along z-axis. Its lower cnd is hnged at
63. A rod ol mass M&length stands about z-ais with an angular vekocity ,
is rotating freelv
ng (B) (D) g2 mass Mand radius R. The whole arangement
the angular speed of the atangemen.
$8. Ihe angular xccleration of the rod is :
4 The rod falls on disc & rotates with disc. Find
oo, R 6o,R
),R 3o,R (D) (+ 6R

$9.
(B)
A pulley syMem is attached toa massless board as show n
41 (D)
(A)F-R
(B) 27+3R?
(C)F+6R
the origin O with a velocity v, at an angle
0. Identify the
below. The board pivots only at the pivot 64. Aprojcctile of mass 'm is thrown from
pont. A 10kg mass M sits cexactly in thc middle of the board. If the angle 9 is 60°. what is the force CORRECT statement:
Fún N) necessary to hold the board in the position shown.

M always zero
(A)Angular momentum of the particle about Ois
momentum of the particle about O increases with time.
(B) Angular
Pivot point clockwise sense.
in the
60. There are two pulleys having radius 3R and R which can rotate freely. Third (C) Aconstant torque acts on the particle about O
pulley is massless string is at thec highest position.
also light. Find the ratio of angular acceleration of pulley having mass Mto pulley (D)Angular momentum of the particle is least when it is
having mass 2M. rod XY of length 2 is hinged at one end X to the floor and stands vertical. When
2M 65. Athin uniform
allowed to fall, the angular speed with which the rod strikes the floor is
M

(B) |21 (D)

V4/
on the
66. Pulley is rotating with angular velocity o. Pulley is sufficiently rough so that string doesnot slip
pulley. Then angular momentum of system (pulley + blocks) about axle of pulley is :

61. A particle of maISS m moves with a constant velocity. Which of the following
statemnents is not correct
about its angular momentum about point 0:

m,
lm

Jlm
B_ (A) lo (B)(m, + m, + Dor (C)(m, t m,)ro + lo (D) (m,r + m,r+ I)o
(A) it is zero when it is at A and moving along OA 67 Two disks are mounted on low-friction bearings on a common shaft. The first disc has rotational inertia
(B) is the same at all points along the line DE Iand is spinning with angular velocity o. The second disc has rotational inertia 21 and is spinning in the
(C) is ot the same magnitude but oppositely directed at B and D same direction as the first disc with angular velocity 20 as shown. The two disks are slowly forced
(D) increases as it moves along the line BC toward each other along the shaft until they couple and have a final common angular velocity ol :
62 Suppose you are standing on the edge of a spinning platform and step off at right angles to the
(radially outward). Now consider it the other way. You are edge
carousel and you step onto the plattorm at right angles to thestanding
on the ground next to a spinning
edge
(A)There is no change in rotational speed of the carousel in either (radially inward).
(B) There is a change in rotational speed in the first situation but notsituation.
the second.
(C) There is a change in rotational speed in the second
situation but not the first (A) (B)
V3 (C) ov7/3 (D) 3o
(D) There is a change in rotational speed in both instances. 3

16 17
 ROTATIONAL MOTION
JEE-Physiks ALLEN ALLEW
speed
position with its bottom on a smooth surface. If vis the
68. The semi circular disc of radius R and mass m is free to rotate about the point O in shown figure.
72. A uniform rod is released from its vertical angle with the horizontal,
angular velocity whenit makes an
string
of centre of mass of the rod and o is its
then :
semi circular
disc mass (m)

mg
(A) Tension in the string is

(B) Angular acceleration of the semi circular disc just after we cut the string is g/4R.
(C) Force due to hinge on the semi circular disc always has non-zero vertical (C)v= cos (D) v= sin 9cos
2
component (A) V= sin 0 (B) v=
(D) Acceleration of center of mass of the semi circular disc just after we cut
the string must
a rough fixed incline plane of angle 0. Choose the correct options
have horizontal & vertical non-zero components. 73. A solid sphere is under pure rolling on
if onlycontact forces and gravity are acting:
sphere rolls up the incline and it will be up the incline if
Paragraph for Question no.69 and 70 (A) Frictional force willbe down the incline if
sphere rolls down the incline.
A disk of radius 2R and mass 'M' is hinged from its center. If a disk of radius R been removed such that
whether spheres rolls up the incline or down the incline
radius of bigger disk behave as a diameter of the disk and it is welded on the opposite side as shown in (B)Frictional force willbe down the incline of incline plane
increase with the increase in angle
diagram. (C) Frictional force and acceleration of the body will
be zero during the
of contact of sphere with incline will
(D) Velocity and acceleration of the point
motion.
on a smooth horizontal
uniform solid cylinder of mass M, which lies
74. A thread is tightly wound over a horizontal force Fas shown. Then acceleration
is pulled by
surface as shown. The free end of the thread
is :
Case-I Case-II of centre of cylinder at the shown instant
69. Find the ratio of moment of inertia about point 'O' in Case-I and Case-II:
(&)
2
(4) (C) T2 (D) I
Smooth horizontal surface
70. Find the angular acceleration of a system in case-II if the system is released from the given position
about the axis passing through O and perpendicular to the plane of disc: 3F 2F
F F (D) M
(B) M (C) 2M
(D)8 (A)
(A) (B) (C) 2M
2R 3R angular velocity o. There is a
horizontal surtace with linear velocity V and
4R
75. A disc of radius R rolls on a vertical diameter measured anticlockwise (see
71. The wheel of radius r= 300 mm rolls to the right without slipping and has a velocity v = 3 m/s of its angle O with upward
point Poncircumference of disc at
center 0. The speed of the point Aon the wheelfor the instant represented in thefigure is : equalto
figure), which has a vertical velocity. Here 0 is

04-200 mm

V
V
(B)-sin! V (C) I - CoS (D)n + cos Ro
(A) n+ sin Ro Ro
Ro
(A) 4.36 m/s (B) 5 m/s (C)3 m/s (D) 1.5 n/s 19
 ROTATIONAL MOTION
JEF-Pysiks ALLEM ALLEN
surface vith a specd v,. The
76. Asoid cy linder and a hollow cylinder of a same mass and radius, both initially at rest. roll downth horizontal direction on a roueh horizontal
.2. Aing of mass m is thrown in
same inclincd plane from same height without slipping. Choose the CORRECT option(s) : speed of the ring. when it start pure rolling, is
-
(A) The hollow cylinder reaches the bottom firs.
(B) The solid cylinder reaches thec bottom firt.
(C) The two cylinders reach the bottom together.
(D) The kinetic energy at the bottom are equal. (D) 3
(B) 3 (C) 3
Paragraph for Question No. 77 to 79 (A)
plane. At some instant it has translational
Consider a spoolof mass 2kg and inner and outer radii of lm and 2n respectively acted by forces F= 1 solidsphere of mass Mand radius r slips on a rough horizontal sphere starts
Nas shown in figure. Moment of inertia of the spool about an axis passing through O and perpendicular10 33. A v, /2r. The translational velocity after the
to the plane of paper is 4 kgm'. velocity v, and rotational velocity about the centre
pure rolling
o= Vo/2r
F
Vo

(B) 6v,/7 in backward direction

(A) 6v/7 in forward direction
7v/6 in forward direction (D) 6v/ 6 in backward direction
(C) impulse P is
rod AB of mass m and length ( is at rest on a smooth horizontal surface. An
84. A uniform
77. The frictional force acting on the body if it performs pure rolling, is : time taken by the rod to turn through a right angle is:
applied to the end B. The
20

78.
(A)3 (B) 3
(); (D) None of these
Thekinetic encrgy of the body after 3 seconds will be:
(A) 75 J (B) 75/2 J (C) 75/4 J (D) 75/8 J PB
79. Ifground is smooth, then the total kinetic energy after 3 seconds will be:
(A) 105.5J 2aml
(B) I12.5J (C) 115.5J (D) None of these 2rmt (D)
(A) (B) (C) 12P 3P
80. The end A of aladder APof length Sm, kept inclined to a vertical wall is P 3P
slipping over a horizontal
surface, when A is at a distance of 3m from the walI. If velocity of centre of slipping down an incline plane of length / and
mass at this moment is 85 A uniform disk of mass m and radius R rolls without
1.25m/s then velocity of the lowest point A of the ladder at this instant is : Its angular momentum about the
inclination 0. Initially the disk was at rest at the top of the incline plane.
bottom will be equal to :
point of contact with the inclined plane when it reaches the
m'R'glsin 0 (D) zero
(A) J4m'R'glsin 0 (B) J3m²R°gl sin 9 (C) 4
0.
m at its one of end as showWn in diagram with e =
80. A particle of mass m strikes with a rod of mass then :
without sticking to the rod. If we observethe rod and particle from the point A on the rod,
(A) 1.25 m/s (B) Om/s (C) Im/s
Twoforces of (D) 2 m/s
81. magnitudef are acting on a unifom disc kept on a
figure. Friction force by the horizonal surface on the disc horizontal rough surface as Show m

collision.
will be conserved just before and just after
(A) Angular monmentum of rod and particle
particle will be conserved.
(B) Linear momentum of rod and
(A)is in forward direction will be pure rotation.
(B)is in (C) Observed motion of rod after collision
(C) is zero backward
(D)depends on thedirection (D) Observedmotion of particle will be straight line after collision.

20 magnitude of F 21
 ROTATIONAL MOTION
JEE-Physics coefficient of t ALLE
87. Asolid sphere of mass 10 kg is placeddon a rough horizontal surface with friction =0.) ANSWER KEY
Ia torce of 28 Nis applied at the top of the sphere then, 7. (A, B, D)
-28N 5. (B) 6. (A)
2. (B) 3.(D) 4. (C)
1.(C) 11. (D) 12. (C)
(A)S, (B) S, (C) P, (D)P, Q, R
8. (D) 9. (B) 10.
u=0.1 18. (B,C) 19. (C)
16. (D) 17. (A)
14. (C) 15. (C)
(A) friction force will be 10 N in forward direction. 13. (B) 23. (C) 24. (B)
21. (B) 22. (C)
(B) friction force will be less than 10N in backward direction.
20. (A)-S, (B)-Q,(C)-P, (D)-R
29 27. (B) 28. (C)
(C)Acceleration of centre of mass will be m/s². 25. (C) 26. (B) 32. (D)
30. 4.8 Ma' 31. (D)
(D) ’ (R)
(D) Acceleration of centre of mass will be 3.8m/s?. 29. (A) (T);(B) ’ (Q); (C) ’ (P, S) ; 39. (C)
88. A disc of mass m radius R is rolling on a rough surface encounters a movable wedge of sufficient heicht 36.(B) 37.(C) 38. (C)
34. (D) 35. (B)
as shown in figure. There is no friction between wedge and ground and also between disc and weion 33.(A) 45. (A) 46. (A,C)
then: 43. (C) 44. (D)
40. (B, C) 41.(D) 42. (A)
52. (C) 53. (A)
50. (C) 51.(C)
47. (A,D) 48. (C) 49. (A)
59. 25 N 60.6
58. (C)
m
y=oRCo 54. (A, B, C) 55. (B, C, D)
56. (A) 57. (B)
66. (C) 67. (A)
64. (B) 65. (B)
62. (C) 63. (B)
61. (D) 73. (C) 74. (B)
(A) Maximum height attained by the disc centre is 71. (A) 72. (C)
4g 68. (A,C,D) 69. (D) 70. (D)
79. (B) 80. (D) 81.(C)
(B) Velocity of wedge when disc reaches maximum height is (v/2) 76. (B, D) 77. (B) 78. (B)
(C) Angular velocity of disc at maximum height will be zero 75. (C,D) 88. (A, B)
86.(C) 87. (A,D)
(D) Velocity of disc at maximum height will be zero 83. (A) 84. (C) 85. (B)
82. (A)
89. In each case, there is sufficient friction for regular rigid uniform body to (D)-Q,R,S
horizontal surface. Now Match the Column I and II undergo pure rolling on arigid 89.(A)-P,R,S; (B)-Q,R,S; (C)-Q,S;
Column-I Column-II

(A) (P) The direction of static friction on the disc is towards

R right.
disc

(B) (Q) The directionof static friction on the

disc is towards left.
disc

(C) (R) The angular

acceleration will be clockwise
disc

(S
(D) Acceleration of the centre mass can be in the
disc direction o
23