Class – 12
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Subject – Mathematics Topic –Rotation (revision) DPP - revision final 1 Date: 30.03.2020
Permutation and combination (Level – I) Date:28.03.2020
Level - I
L
1. A slender rod of mass M and length L hinged at O is kept O A
horizontal and then released. The other end of the rod M
strikes a solid sphere of mass M and radius R (at point P)
L
kept on a smooth horizontal surface. The points O and P
are on the same vertical line. After the collision, the rod MR
comes to rest. The angular speed of the sphere after the P
collision is
=0
3g R 3g
(A) L (B) L L
L 3g
(C) R L (D) zero
2. The angular velocity of a body changes from 9 rad/sec to 1 rad/sec without applying a torque but due to the
change in its moment of inertia about a particular axis. The ratio of radii of gyration about that particular axis in
the two cases is
(A) 9 : 1 (B) 1 : 3
(C) 3 : 1 (D) 1 : 9
3. Four particles are attached to the ends of two massless rods. M
The rods are connected at point O as shown in the figure. The
system can rotate about an axis perpendicular to the plane of L /2
w
the paper and passing through O. If, starting from rest under O M
M
the action of a constant net external torque having L /4 3 L /4
magnitude MgL, the system rotates about that axis, then at L /2
what time will its angular speed become w?
M
5L 2L
8g 3g
(A) (B)
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9L 5 L
8g 3g
(C) (D)
4. A 5 m long pole of 3 kg mass is placed against a smooth =0
vertical wall as shown in the figure. Under equilibrium 5m
condition, if the pole makes an angle of 37 with the
37 0
horizontal, the frictional force between the pole and
horizontal surface is
(A) 20 N (B) 30 N
(C) 20 N (D) 30 N
5. The moment of inertia of NaCl molecule with bond length r about an axis perpendicular to the bond and passing
through the centre of mass is
mNa mCl 2
r
mNa mCl
(A) (mNA + mCl)r2 (B)
mNa mCl 2 mNa mCl 2
r r
mNa mCl mNa mCl
(C) (D)
6. Two particles A and B start moving simultaneously in the same direction along two parallel lines separated by a
distance l. A starts moving with a constant velocity v 0 while B starts moving with a constant acceleration a .
Which of the following graph may represent the magnitude of the angular momentum of A with respect to B
versus time?
(A) (B)
LA/B LA/B
t t
(C) (D)
LA/B
LA/B
t t
7. Moment of inertia of a uniform semicircular ring of mass M and radius R about an axis passing through its center
of mass and perpendicular to the plane of the ring is
MR2
(A) 2 (B) MR2
4 4
1 2 1 2
(C) MR2 (D) MR2
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8. When there is no external torque acting on a body moving in elliptical path, which of the following quantities
remain constant?
(A) Kinetic energy (B) Potential energy
(C) Linear momentum (D) Angular momentum
9. A solid sphere of mass M and radius R is placed vertically on a rough M
horizontal surface. If a horizontal force F is applied at a distance R/6 R
(R/6)
below the centre line parallel to the diameter of the sphere, the F
direction of frictional force will be
(A) forward (B) backward
(C) depends upon value of F (D) insufficient information
10. A uniform ring of mass m and radius r is hinged at point O so that it
can rotate about the horizontal axis passing through O in vertical O
plane. If the system is released from rest, then the initial acceleration
of the centre of mass of the ring is [Ring is in the vertical plane.]
(A) g (B) g/2
(C) g/4 (D) g/8
11. An equilateral thin plate of side ‘a’ is supported at A and B. If A is A a B
removed at time t = 0, which of the following is correct at t = 0?
Take instantaneous angular acceleration as a and instantaneous a a
angular velocity as w about the hinge B.
(A) a = 0, w ¹ 0 (B) a ¹ 0, w ¹ 0
(C) a ¹ 0, w = 0 (D) a = 0, w = 0
12. A semi-circular disc of radius 1 m and mass = 4 kg is lying on Y
the horizontal x-y plane. If XX¢ is the axis of rotation of the
P
body and a force = 2 N k̂ is applied at point P, the 30 R
X X
magnitude of angular acceleration is equal to (the region is
gravity free)
(A) 2 rad/s2 (B) 3 rad/s2
(C) 1 rad/s2 (D) 4 rad/s2
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13. A cubical box of side length L rests on a rough horizontal surface F
having coefficient of friction m. A variable horizontal force F = at B
where a is a constant and t is time, is applied on the top of the block
as shown in the figure. The coefficient of friction is sufficient so that
the block does not slide before toppling. The graph between torque
due to normal reaction about end B and time before toppling start is
(A) (B)
t t
(C) (D) none of these
14. A disc is having a pure rolling motion on a moving plank as shown
r u
in the figure. Choose the correct option from the following.
v
(A) u r = v (B) u r v = 0
(C) u = r + v (D) none of these
15. A sphere of radius R and mass M collides elastically with a
C M
cubical block of mass M and side 2R. All the surfaces of the R
system are smooth. Given that the sphere was rolling
without slipping with an angular velocity w at the time of
collision. The velocities of the sphere and the block after the
collision are
sphere 0, v sphere 0, v block v sphere , v sphere 0, v block v
(A) (B)
v v
sphere 0, v sphere 0, v block 0 sphere , v sphere , v block
(C) (D) 2 2 2
16. A uniform meter stick of mass m is pivoted about a horizontal
axis through its lower end O. Initially, it is held vertical and is
60
allowed to fall freely. Its angular velocity at the instant when it
makes an angle of 60 with the vertical is
O
g 3g
(A) 3 (B) 2
g 2g
(C) 4 (D) 3
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17. There is a uniform circular ring of mass m. A particle of mass m is
placed at its centre and is connected to the rim by rigid light spokes. If
this assembly is placed on a rough inclined surface, then frictional
force acting on the assembly, if it undergoes pure rolling, is
1 2
(A) 3 mg sin q (B) 3 mg sin q
1 1
(C) 6 mg sin q (D) 2 mg sin q
Level – I(ANSWERS):
1. D 2. B 3. C 4. A
5. C 6. B 7. C 8. D
9. B 10. B 11. C 12. C
13. B 14. B 15. B 16. B
17. B
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