Two solid cylinders P and Q of same mass and same radius start rolling down a fixed 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 (s) is (are) correct ?

(a) Both cylinder 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

Concept Questions :-

Rolling motion
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A solid sphere is rolling on a frictionless surface, shown in figure with a translational velocity v m/s. If sphere climbs up to height h then value of v should be -

(a) $\ge \sqrt{\frac{10}{7}\mathrm{gh}}$                                                    (b) $\ge \sqrt{2\mathrm{gh}}$

(c) $2\mathrm{gh}$                                                              (d) $\frac{10}{7}\mathrm{gh}$

Concept Questions :-

Rolling motion
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A soldier is firing 20 bullets per second from his gun having a muzzle speed of 150 m/s. The mass of each bullet is 50 g. If they strike the wall and rebound with the same speed, then the force on the wall is

1.  75 N

2.  150 N

3.  300 N

4.  600 N

Concept Questions :-

Linear momentum
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The projectile breaks into fragments at the highest point of motion

Concept Questions :-

Torque
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The value of M, as shown, for which the rod will be in equilibrium is (rod is massless)

1.  1 kg

2.  2 kg

3.  4 kg

4.  6 kg

Concept Questions :-

Torque
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The minimum coefficient of friction for a solid sphere to roll without slipping on an inclined plane of inclination 45$°$ is

1.  2/7

2.  1/3

3.  1/2

4.  2/5

Concept Questions :-

Rolling motion
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A wheel is rolling along a horizontal ground with a speed o 10 m/s. The magnitude of the velocity of the points at the extremities of the horizontal diameter of the wheel is equal to

(1)

(2) 10 m/s

(3)

(4)

Concept Questions :-

Rolling motion
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A projectile of mass 50 kg is shot vertically upwards with an initial velocity of 100ms-1. After 5 seconds it explodes into two fragments, one of which having mass 20 kg, travels vertically up with a velocity of 150 ms-1. The velocity of the other fragment at that instant is -          [Take g= 9.8 m/${s}^{2}$]

1.  100 ms-1

2.  150 ms-1

3.  -150 ms-1

4.  -15 ms-1

Concept Questions :-

Linear momentum
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A sphere of mass m moving with constant velocity hits another sphere of the same mass at rest. If e is the coefficient of restitution. The ratio of their velocities after the collision is

1.  1 + e

2.

3.

4.

Concept Questions :-

Linear momentum
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Concept Questions :-

Angular momentum
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