If the angular momentum· of a particle of mass m rotating

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 Multiple Choice QuestionsMultiple Choice Questions

31.

A torque of 1 N-m is applied to a wheel which is at rest. After 2 second the angular momentum in kg-m2 /s is

  • 0.5

  • 1

  • 2

  • 4


32.

The position vectors of two identical particles with respect to the origin in three-dimensional coordinate system are r1 and r2. The position vector of centre of mass of the system is given by

  • r1 + r2

  • 2(r1 + r2)

  • r1 − r2

  • r1 + r22


33.

If a body of moment of inertia 2 kg m2 revolves about its own axis making 2 rotations per second, then its angular momentum (in Js) is

  • 2 π

  • 4 π

  • 6 π

  • 8 π


34.

A rigid body is the one in which

  • it can have only rotational motion

  • it can have only translational motion

  • the distances between all pairs of particles of the body do not change

  • its centre of mass always lies inside the material of the body


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35.

Two objects P and Q initially at rest move towards each other under mutual force of attraction. At the instant when the velocity of P is v and that of Q is 2v, the velocity of centre of mass of the system is

  • v

  • 3v

  • zero

  • 1.5 v


36.

A body rolls down an inclined plane . If its kinetic energy of rotation is 40% of its kinetic energy of translation motion, then the body is

  • hollow cylinder

  • ring

  • solid disc

  • solid sphere


37.

A circular disc A and a ring B have same mass and same radius. If they are rotated with the same angular speed about their own axis, then

  • A has less moment of inertia than B

  • A has less rotational kinetic energy than B

  • A and B have the same angular momentum

  • A has greater angular momentum than B


38.

Two discs rotating about their respective axis of rotation with angular speed 2 rad s-1 and 5 rad s-1 are brought into contact such that their axes of rotation coincide. Now, the angular speed of the system becomes 4 rads-1 . If the moment of inertia of the second disc is 1 x 10-3 kg m2 then the moment of inertia of the first disc (in kg m2) is

  • 0.25 × 10-3

  • 1.5 × 10-3

  • 0.5 × 10-3

  • 0.75 × 10-3


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39.

A wheel is rotating at 1800 rpm about its own axis. When the power is switched off, it comes to rest in 2 min. Then, the angular retardation in rads-1 is

  • 2π

  • π

  • π/2

  • π/4


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40.

If the angular momentum· of a particle of mass m rotating along a circular path of radius r with uniform speed is L, the centripetal force acting on the particle is

  • L2mr3

  • L2mr

  • Lmr2

  • L2mr


A.

L2mr3

Angular momentum

          L = Iω

where  I = mr2   and   ω = vr

          L = mr2 × vr

          L = mvr                .......... (i)

Centripetal force,

          F = mv2rF = mr . Lmr2                         From Eq. (i)F = mL2r . m2 . r2  F = L2mr3 


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