Angular Momentum and its Conservation for a Rigid Body
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PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365637 A body of mass \(m\) and radius \(r\) is released from rest along a smooth inclined plane of angle of inclination \(\theta\). The angular momentum of the body about the instantaneous point of contact after a time \(t\) from the instant of release is equal to

1 \(m g r t \cos \theta\)
2 \(\left(\dfrac{3}{2}\right) m g r t \sin \theta\)
3 \(m g r t \sin \theta\)
4 None of these
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365638 A disc of mass \(M\) and radius \(R\) is rolling with angular speed \(\omega\) on a horizontal plane as shown in the figure. The magnitude of angular momentum of the disc about the origin \(O\) is
supporting img

1 \(2 M R^{2} \omega\)
2 \(\dfrac{1}{2} M R^{2} \omega\)
3 \(\dfrac{3}{2} M R^{2} \omega\)
4 \(M R^{2} \omega\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365639 Assertion :
For the planets orbiting around the sun, angular speed, linear speed and K.E. change with time, but angular momentum remains constant.
Reason :
No torque is acting on the rotating planet. So its angular momentum is constant.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365640 A child is standing with folded hands at the centre of a platform rotating about its central axis. The kinetic energy of the system is \(K\). The child now stretches his arm so that moment of inerita of the system doubles. The kinetic energy of the system now is:

1 \(2 \mathrm{~K}\)
2 \(\dfrac{K}{2}\)
3 \(\dfrac{K}{4}\)
4 \(4 \mathrm{~K}\)
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PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365637 A body of mass \(m\) and radius \(r\) is released from rest along a smooth inclined plane of angle of inclination \(\theta\). The angular momentum of the body about the instantaneous point of contact after a time \(t\) from the instant of release is equal to

1 \(m g r t \cos \theta\)
2 \(\left(\dfrac{3}{2}\right) m g r t \sin \theta\)
3 \(m g r t \sin \theta\)
4 None of these
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365638 A disc of mass \(M\) and radius \(R\) is rolling with angular speed \(\omega\) on a horizontal plane as shown in the figure. The magnitude of angular momentum of the disc about the origin \(O\) is
supporting img

1 \(2 M R^{2} \omega\)
2 \(\dfrac{1}{2} M R^{2} \omega\)
3 \(\dfrac{3}{2} M R^{2} \omega\)
4 \(M R^{2} \omega\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365639 Assertion :
For the planets orbiting around the sun, angular speed, linear speed and K.E. change with time, but angular momentum remains constant.
Reason :
No torque is acting on the rotating planet. So its angular momentum is constant.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365640 A child is standing with folded hands at the centre of a platform rotating about its central axis. The kinetic energy of the system is \(K\). The child now stretches his arm so that moment of inerita of the system doubles. The kinetic energy of the system now is:

1 \(2 \mathrm{~K}\)
2 \(\dfrac{K}{2}\)
3 \(\dfrac{K}{4}\)
4 \(4 \mathrm{~K}\)
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PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365637 A body of mass \(m\) and radius \(r\) is released from rest along a smooth inclined plane of angle of inclination \(\theta\). The angular momentum of the body about the instantaneous point of contact after a time \(t\) from the instant of release is equal to

1 \(m g r t \cos \theta\)
2 \(\left(\dfrac{3}{2}\right) m g r t \sin \theta\)
3 \(m g r t \sin \theta\)
4 None of these
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365638 A disc of mass \(M\) and radius \(R\) is rolling with angular speed \(\omega\) on a horizontal plane as shown in the figure. The magnitude of angular momentum of the disc about the origin \(O\) is
supporting img

1 \(2 M R^{2} \omega\)
2 \(\dfrac{1}{2} M R^{2} \omega\)
3 \(\dfrac{3}{2} M R^{2} \omega\)
4 \(M R^{2} \omega\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365639 Assertion :
For the planets orbiting around the sun, angular speed, linear speed and K.E. change with time, but angular momentum remains constant.
Reason :
No torque is acting on the rotating planet. So its angular momentum is constant.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365640 A child is standing with folded hands at the centre of a platform rotating about its central axis. The kinetic energy of the system is \(K\). The child now stretches his arm so that moment of inerita of the system doubles. The kinetic energy of the system now is:

1 \(2 \mathrm{~K}\)
2 \(\dfrac{K}{2}\)
3 \(\dfrac{K}{4}\)
4 \(4 \mathrm{~K}\)
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PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365637 A body of mass \(m\) and radius \(r\) is released from rest along a smooth inclined plane of angle of inclination \(\theta\). The angular momentum of the body about the instantaneous point of contact after a time \(t\) from the instant of release is equal to

1 \(m g r t \cos \theta\)
2 \(\left(\dfrac{3}{2}\right) m g r t \sin \theta\)
3 \(m g r t \sin \theta\)
4 None of these
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365638 A disc of mass \(M\) and radius \(R\) is rolling with angular speed \(\omega\) on a horizontal plane as shown in the figure. The magnitude of angular momentum of the disc about the origin \(O\) is
supporting img

1 \(2 M R^{2} \omega\)
2 \(\dfrac{1}{2} M R^{2} \omega\)
3 \(\dfrac{3}{2} M R^{2} \omega\)
4 \(M R^{2} \omega\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365639 Assertion :
For the planets orbiting around the sun, angular speed, linear speed and K.E. change with time, but angular momentum remains constant.
Reason :
No torque is acting on the rotating planet. So its angular momentum is constant.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365640 A child is standing with folded hands at the centre of a platform rotating about its central axis. The kinetic energy of the system is \(K\). The child now stretches his arm so that moment of inerita of the system doubles. The kinetic energy of the system now is:

1 \(2 \mathrm{~K}\)
2 \(\dfrac{K}{2}\)
3 \(\dfrac{K}{4}\)
4 \(4 \mathrm{~K}\)
NEET DIGITAL LIBRARY