- A y wheel of moment of inertia 3 × 10^2 kg m^2 is
rotating with uniform angular speed of 4.6 rad s–1.
If a torque of 6.9 × 10^2 N m retards the wheel, then
the time in which the wheel comes to rest is
(a) 1.5 s (b) 2 s (c) 0.5 s (d) 1s - A particle of mass m moves in the XY plane with a
velocity v along the straight line AB. If the angular
momentum of the particle with respect to origin O
is LA when it is at A and LB when it is at B, then
(a) LA > LB (^) Y
O X
B
(b) L A
A = LB^
(c) e relationship between
LA and LB depends upon
the slope of the line AB
(d) LA < LB
- Two solid cylinders P and Q of same mass and same
radius start rolling down a xed inclined plane from
the same height at the same time. Cylinder P has
most of its mass concentrated near its surface, while
Q has most of its mass concentrated near the axis.
Which statement is correct?
(a) Both cylinders P and Q reach the ground at the
same time.
(b) Cylinder P has larger linear acceleration than
cylinder Q.
(c) Both cylinder P and Q reaches the ground with
same translational kinetic energy.
(d) Cylinder Q reaches the ground with larger
angular speed. - A circular platform is mounted on a frictionless
vertical axle. Its radius R = 2 m and its moment of
inertia about the axle is 200 kg m^2. It is initially at
rest. A 50 kg man stands on the edge of the platform
and begins to walk along the edge at the speed of
1 m s–1 relative to the ground. Time taken by the
man to complete one revolution is
(a) p s (b)^3
2
πs (c) 2p s (d) π
2s- Two spherical bodies of mass M and 5 M and radii R
and 2R released in free space with initial separation
between their centres equal to 12 R. If they attract
each other due to gravitational force only, then
the distance covered by the smaller body before
collision is
(a) 4.5 R (b) 7.5 R (c) 1.5 R (d) 2.5 R - Two masses m 1 and m 2 (m 1 > m 2 ) are connected by
massless exible and inextensible string passed over
massless and frictionless pulley. e acceleration of
centre of mass is
(a) mm
mm(^12) g
12
2
−
(b)mm
mm(^12) g
12
−
+
(c)mm
mm(^12) g
12
+
−^ (d) Zero
Assertion & Reason Type
Directions : In the following questions, a statement of assertion
is followed by a statement of reason. Mark the correct choice as:
(a) If both assertion and reason are true and reason is the
correct explanation of assertion.
(b) If both assertion and reason are true but reason is not the
correct explanation of assertion.
(c) If assertion is true but reason is false.
(d) If assertion is false but reason is true.- Assertion : Two axes AB and CD are as shown in
gure. Given gure is of a semi-circular ring. As the
axis moves from AB towards CD, moment of inertia
rst decreases, then increases.
A B
C D
Reason : Centre of mass lies somewhere between
AB and CD.- Assertion : A ring and a disc of same mass and
radius begin to roll without slipping from the top
of an inclined surface at t = 0. e ring reaches the
bottom of incline in time t 1 while the disc reaches
the bottom in time t 2 , then t 1 < t 2.
Reason : Disc will roll down the plane with more
acceleration because of its lesser value of moment
of inertia. - Assertion : Two identical
spherical spheres are half
lled with two liquids of
densities ρ 1 and ρ 2 (> ρ 1 ).
e centre of mass of both the spheres lie at same level.
Reason : e centre of mass will lie at centre of the
sphere.
JEE MAIN / ADVANCED
Only One Option Correct Type - Each pulley in gure has radius r and moment of
inertia I. e acceleration of the block is
m
M(a) (b)