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

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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) 210  m/s

(2) 10 m/s

(3) 10 m/s

(4) 102 m/s

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/s2]

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.  1 + e2

3.  1 + 2e1 - 2e

4.  1 - e1 + e

Concept Questions :-

Linear momentum
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A body of mass m is projected at a velocity v0with an angle of projection θ. Angular momentumL of body after time t w.r.to origin is proportional to:1. Lt                                     2. Lt23. Lt0                                    4. Lt

Concept Questions :-

Angular momentum
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A mass M is moving with constant velocity parallel to the X-axis. Its angular momentum w.r.t. origin is:

1.  Zero

2.  Remains constant

3.  goes on increasing

4.  goes on decreasing

Concept Questions :-

Angular momentum
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A pulley of mass m & radius R is free to rotate about its axis which is horizontal. A string is wound around it and mass m is attached to its free end. When mass m falls through a distance h, its speed at that instant is:

                                               

1.  proportional to R

2.  proportional to 1/R

3.  proportional to 1/R2

4.  independent of R

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If I is the moment of inertia of a solid sphere about an axisparallel to a diameter of sphere and at a distance x from it.Which of the following graph represents the variation of Iwith x?

Concept Questions :-

Moment of inertia
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A particle is rotating under the central force, in which one of the following quantities is constant:

1.  torque

2.  angular momentum

3.  linear momentum

4.  none of these

Concept Questions :-

Angular momentum
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