PHYSICS TEST
ROTATORY MOTION
01.
02.
A disc having radius r = 2m is placed on smooth horizontal surface velocity of point A and B is
given as shown in figure. Distance between point O and axis of rotation at that particular instant
A
4 m/sec
of time.
A) 1 m
O
B) 0.5 m
C) 0.25 m
B
1.5 m/sec
D) 2 m
A particle of mass M is moving in a horizontal circle of radius R with a uniform speed V. When
it moves from one point to a diametrically opposite point, its
MV 2
4
A) Kinetic energy changes by
03.
C) Momentum changes by 2MV
D) Kinetic energy changes by MV2.
The moment of inertia of a uniform rod about an axis passing through its centre-of-mass and
making an angle of 30º with the rod is (m: mass of rod, : length of rod)
A)
04.
1
m
12
C) h 
06.
2
B)
1
m
16
2
C)
1
m
48
2
D) None of the above
A particle of mass m attached to the end of string of length is released from the initial position
A as shown in the figure. The particle moves in a vertical circular path about O. When it is
vertically below O, the string makes contact with nail N placed directly below O at distance h
and rotates around it. If the particle just complete the vertical circle about N, then
A) h 
05.
B) Momentum does not change
3
5
5
2
5
4
D) h  .
5
B) h 
A force F acts horizontally at the highest point of a solid sphere of mass ‘m’ kept on a rough
horizontal plane. If the sphere rolls without slipping, find the acceleration of centre of the
sphere.
A) 5F/7m
B) 7F/5m
C) 7F/10 m
D) 10F/7m
A rod of length is pivoted at one of the ends and is made to rotate in a horizontal plane as
shown in figure with a constant angular speed. A ball of mass m is suspended by a string of
length from the other end of the rod. If the angle made by the string with the vertical is  then
determine angular speed   .
A)
g
(1  sin )
B)
g
cos 
C)
g tan 
(1  sin )
D)
g cot 
(1  cot )
1
07.
08.
A spot light is fixed 4m from the vertical wall and is rotating at a rate 1 rads –1. The spot moves
horizontally on the wall. Find the speed of the spot on the wall when spot light makes an angle
of 45° with the wall.
A) 4 ms–1
B) 6 ms–1
C) 8 ms–1
D) none of these
An inclined plane ends into a loop of radius r. Find the minimum height from where a particle
shall slip so as to loop the loop.
A)
09.
10.
11.
5r
2
5r
3
C)
a
D)
4a
10
r
3
3a
A rigid body rotates about a fixed axis with variable angular velocity equal to    t  at time‘t’
where  ,  are constants. The angle through which it rotates before it stops is




A)
B)
C)
D)

2
2
2 2
A constant power is supplied to a rotating disc. Angular velocity   of the disc varies with
2
2
13.
5r
4
A particle slips from a height 4r from an inclined plane which ends into a loop of radius r. Find
the normal reaction at the highest point and at the lowest point.
A) 3 mg, 9 mg
B) 3 mg, 6 mg
C) 0, 6 mg
D) 4 mg, 8 mg
A particle has velocity 2rg at the highest point in a vertical circle of radius r. Find the ratio of
the normal reactions at the highest to the lowest points.
A) 1/7
B) 1/3
C) 1/5
D) 2/9
A uniform rod AB of mass ‘m’ and length ‘2a’ is falling freely without rotation under gravity
with AB horizontal. Suddenly the end A is fixed when the speed of the rod is  . The angular
speed with which the rod begins to rotate is

3
3
4
A)
B)
C)
D)
4a
12.
B)
number of rotations  n  made by the disc as
14.
A)  n3
B)  n2
C)   n1/3
D)   n
Velocity of centre of smaller cylinder is v . There is no slipping anywhere. The velocity of centre
of the larger cylinder is ____________
R
2R
a) 2v
b) v
c)
2
3v
2
d) 5 v
v
15.
A system of uniform cylinders and plates is shown. All the cylinders are identical and there is no
slipping at any contact. Velocity of lower and upper plates is v and 2v respectively as shown.
Then the ratio of angular speeds of the upper cylinder to lower cylinder ____________
2v
v
A)
16.
1
2
B) 3
C)1
D) None of these
The spool shown in figure is placed on a rough horizontal surface and has inner radius r and
outer radius R. The angle  between the applied force and the horizontal can be varied. The
critical angle   for which the spool does not roll and remains stationary is given by:
F
R
r
r
 
A)
18.
 2r 

 R
r
r
D)   sin 1
R
R
A solid sphere of mass M and radius R is initially at rest. Solid sphere is gradually lowered on to
a truck moving with constant velocity. What is the final speed of sphere’s centre of mass in
ground frame when eventually pure rolling sets in ________ (where vo is the speed of truck)
A)   cos 1  
R
17.

5v0
7
B)   cos 1 
B)
2v0
7
C)   cos1
C)
7v0
5
D)
7v0
2
A sphere is placed rotating with its centre initially at rest in a corner as shown in figures (a) and
1
3
(b). Coefficient of friction between all the surfaces and the sphere is . Then the ratio of the
friction forces
fa
by ground in situations (a) and (b) is __________
fb
fig ( a)
A) 1
B)
9
10
fig (b )
C)
3
10
9
D) None of these
19.
A wheel is rolling without slipping towards right on a horizontal surface with a linear velocity v .
Then the velocity of a point towards right whose height is equal to the radius of the wheel is ___
A) v
20.
21.
23.
rad
s
v
2
is also moving forward with a
1
7
B)
2
7
C)
3
7
D)
4
7
A solid ball starts from rest and rolls a 30º inclined plane. How much time would it take to cover
7m?
A) 1s
B) 2s
C) 3s
D) 4s
A disc rolls on a table without slipping. Then the fraction of its kinetic energy which is
rotational is ______
B)
1
3
C) 2
D) None
A solid cylinder i) Slides down and ii) rolls down an inclined plane. Then the ratio of
accelerations in the two cases is ___________
A)
25.
D)
2v
velocity 4m / s on a horizontal table. Find the velocity of slipping.
A) 2m / s
B) 1m / s
C) 3m / s
D) Zero
A solid spherical ball rolls on a table without slipping. What fraction of its total kinetic energy is
associated with rotation?
A) 3
24.
C)
A wheel of radius 1m is rotating with angular velocity 5
A)
22.
B) 2v
2
3
B)
3
2
C)
7
2
D) 3
A solid metal ball of mass m is put at the top of the top of inclined plan attached to a curved
track of height nR whose lower portion is in the shape of the circle of radius R of as shown
figure. Then the velocity of the ball when it just rolls to the height R upto the point B is _____
C
B
nR
A
10
5
1
gR  n  1
gR  n  1
gRn
C)
D)
7
7
7
A hoop rolls over a horizontal surface without slipping with constant velocity v. Find the
velocity of a point A of the hoop at the instant the line OA joining A with centre O, makes
and angle 2  with the vertical?
A)
26.
ngR
B)
B
A
2
O

O'
A) 2v
B) 2v cos 
C) v cos 
4
D) v cos 2
v
2
v
27.
28.
29.
A solid sphere rolls up on inclined plane of inclination 30º. At the bottom of the incline the
sphere has a speed of 7m / s . How far will the sphere travel up the plane?
A) 5m
B) 6m
C) 7m
D) 8m
A disc of radius R spins on its own axis at a constant angular velocity 0 and is gently lowered
on a level floor. If the coefficient of friction is µ, find the time that would elapse before pure
rolling starts.
R
R
3 R
1
A) t  0
B) t 
C) t  0
D) t  0
0
g
3 g
g
A string of negligible thickness is wrapped several times around a cylinder kept on round
horizontal surface. A man standing at a distance l from the cylinder holds one end of string.
The man pulls the string so that the cylinder moves towards him. What length of string man
must pull to bring the cylinder up to his hand?
.
30.
A) l
B) 2l
C) 3l
D) 4l
A uniform circular disc of mass 200g and radius 4.0cm is rotated about one of its diameter at an
angular speed of 10 rad/s. Find the kinetic energy of the disc.
A) 8mJ
B) 16mJ
C) 4mJ
D) 0.8mJ
5
KEY
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
B
C
C
D
D
C
C
A
A
A
C
B
C
B
B
A
B
B
C
B
B
B
B
B
B
B
C
A
B
C
6
SOLUTIONS
01.
02.
03.
04.
05.
B
C
C
D
D
F + f = ma ….. (1)
F
f
F  f R 
06.
2
a
MR 2
…… (2)
5
R
C
T cos   mg , T sin  
07.
By (1) and (2) we get a 
mv 2
.
r
C
x
 tan 
y
x  y tan  Then differentiate it.

08.
A
mgh =
09.
1
mv 2
2
A
mv 2
N
 mg cos 
r
10.
11.
12.
13.
14.
15.
A
C
B
    t

d
   and at t 
it stops
dt

2
2
  2   
2
C
P   .
 d 
P  I .  .

 d 
Pd  I  2 d 
Integrating above relation  3 
B
Equate the tangential velocity at the rims.
B
7
10F
7m
In the absence of slipping, velocities of contacts points of upper cylinders and lower cylinders
are respectively
v AB 3v

AB 2 R
v
v
wlower = CD 
CD 2 R
wup =

16.
wup
wlower
3
A
If spool is not to translate F cos   f ........1
If spool is not to rotate F.r  FR.........2
 F cos   f And Fr  F  R
 cos  
17.
r
r
   cos 1  
R
R
B
In reference frame of truck angular
Momentum is conserved about P
2
MvR  Mv0 R  MR 2 ......1
5
And for pure rolling v0  R.......2
5
7
1 and 2 v0  v
2
5
Note that v0 is speed in truck frame, in ground frame velocity is =  v  v
=
18.
2
v.
7
B
From fig (a)  N1  N2  mg.....1
N1   N 2 .......2
mg
1  2
3
 f a  mg
10
 N2 
From fig (b) N1  0 : N 2  mg  fb   N 2 

19.
mg
3
fa 9

f b 10
C
vc  v 2  v 2  2v
20.
B
21.
B
vA  vcm   R  4  5 1  1m / s
8
1 2
I
RotaionalKE
2
f 

1 2 1 2
ToatalKE
mv  I 
2
2
22.
B
a
23.
g sin 
1
 3.5 And s  at 2  t  2s
2
K
2
1 2
R
B
1 2
mv
1
Fraction = 4

3 2 3
mv
4
24.
B
a1  g sin  ; a2 
25.
B
mg  nR  
1 2 1 2
2
mv  I   mgR Where I  mR 2 and v  R
2
2
5
10
gR  n  1
7
v
26.
a
g sin 
 1  3/ 2
2
2
1 k / R
a2
B
AD  OA And AC  OB
 CAD  AOB  2
B
A
2
v
2
v
O

O'
 v  v 2  v 2  2vv cos 2
2
A
 vA  2v cos 
27.
C
a
28.
g sin  5 g

sin 
k2
7
1
R2
And v 2  u 2  2as  s  7m
A
1
2
 2 g 
  0   t   0  
t
 R 
f
a
  g  v  o  at   gt......2
M
  I   fR Where I  MR 2   
2  g
R
9
29.

 2 g  
And for pure rolling v     gt   o  
t  R
 R  

R
t  0
3 g
B
Let the cylinder move with linear velocity v . Then the distance moved by centre of mass= l
1
t  ; As the velocity at the top most point of cylinder is 2v, the length of the string pulled
v
during the time = t  l / v is

2v
v
L   2v  t   2v  l / v   2l
30.
C
KE =
1 2
I
2
10