Physics - Rotational Motion and Moment of Inertia

Question - 1

Let m be mass of particle rotating along a circular motion of radius R, L its angular momentum about the centre of circle and \(\omega\) be its uniform angular velocity. Then the kinetic energy of the particle of mass m rotating at a radius R about a fixed centre is

  • A \(\frac { 1 }{ 2 } m{ L }^{ 2 }{ \omega }^{ 2 }\)
  • B \(\frac { 1 }{ 2m } .\frac { { L }^{ 2 } }{ { R }^{ 2 } } \)
  • C \(\frac { { L }^{ 2 } }{ 2m } \)
  • D \(\frac { { L }^{ 2 } }{ 2m{ R }^{ 2 } } \)

Question - 2

Two particles that have equal masses are connected by a thin rod (with neligible mass) and rotate about an axis through the centre of the rod and perpendicular to it. The length of the rod is increased by 13 parts in 106 because of a temperature rise. The fractional change in the angular velocity will be

  • A 26 X 10-6
  • B -26 X 10-6
  • C 13 X 10-6
  • D -13 X 10-6

Question - 3

A 300-g particle is confined to moving in a circular path of radius 25 cm. The application of a constant tangential (linear) force of 1.5 N causes the particle to decelerate from an initial speed of 8 ms-1. The magnitude of angular velocity 2 seconds after the aontinuous application of the force is

  • A 20 rad s-1
  • B 72 rad s-1
  • C 6 rad s-1
  • D 8 rad s-1

Question - 4

A homogeneous sphere rolling on a horizontal surface is in a condition of

  • A stable equilibrium
  • B unstable equilibrium
  • C neutral equilibrium
  • D dynamic equilibrium

Question - 5

A particle in a condition of

  • A stable equilibrium when the potential energy has a minimum.
  • B unstable equilibrium when the potential energy has a maximum.
  • C neutral equilibrium when a small displacement causes no change in the potential energy
  • D All of the above statements are correct

Question - 6

Two unlike parallel forces \(\vec { P } and\quad \vec { Q } ,\quad (\vec { P } >\vec { Q } )\) act at points x unit apart. If the direction of \(\vec { P } \) is reversed, the resultant is displaced through a distance 

  • A \(\frac { 2PQ }{ { P }^{ 2 }-{ Q }^{ 2 } } x\quad unit\)
  • B \(\frac { 2P }{ P-Q } x\quad unit\)
  • C \(\frac { 2Q }{ P-Q } x\quad unit\)
  • D \(\frac { 2PQ }{ { P }^{ 2 }+{ Q }^{ 2 } } x\quad unit\)

Question - 7

Find the torque of a force \(\vec { F } =\quad -3\overset { \wedge }{ i } +\overset { \wedge }{ j } +5\overset { \wedge }{ k } \) acting at the point \(\vec { r } =\quad -7\overset { \wedge }{ i } +3\overset { \wedge }{ j } +\overset { \wedge }{ k } \)

  • A \(14\overset { \wedge }{ i } -38\overset { \wedge }{ j } +16\overset { \wedge }{ k } \)
  • B \(4\overset { \wedge }{ i } +4\overset { \wedge }{ j } +6\overset { \wedge }{ k } \)
  • C \(-14\overset { \wedge }{ i } +38\overset { \wedge }{ j } -16\overset { \wedge }{ k } \)
  • D \(-21\overset { \wedge }{ i } +3\overset { \wedge }{ j } +5\overset { \wedge }{ k } \)

Question - 8

The angular momentum of a body increase by 100% without change in moment of inertia about the given axis of rotation, the increase in its rotational kinetic energy is

  • A 100%
  • B 200%
  • C 300%
  • D 33%

Question - 9

The change in angular momentum is form 1 Js to 4 Js in 4 seconds. Then torque is

  • A \(\frac { 3 }{ 4 } J\)
  • B J
  • C \(\frac { 5 }{ 4 } J\)
  • D \(\frac { 4 }{ 3 } J\)

Question - 10

Before jumping in water from a height, a swimmer bends his body to

  • A increase moment of inertia
  • B decrease moment of inertia
  • C decrease moment of inertia and angular momentum
  • D decrease the angular velocity
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