01. Angular Displacement, Velocity and Acceleration
Rotational Motion

149773 A thin circular ring of mass \(M\) and radius \(R\) rotates about an axis through its centre and perpendicular to its plane, with a constant angular velocity \(\omega\). Four small spheres each of mass \(m\) (negligible radius) are kept gently to the opposite ends of two mutually perpendicular diameters of the ring. The new angular velocity of the ring will be

1 \(4 \omega\)
2 \(\frac{M}{4 m} \omega\)
3 \(\left(\frac{M+4 m}{M}\right) \omega\)
4 \(\left(\frac{M}{M-4 m}\right) \omega\)
5 \(\left(\frac{M}{M+4 m}\right) \omega\)
Rotational Motion

149775 A uniform rod of length \(60 \mathrm{~cm}\) is placed with one end in contact with the horizontal table and is then inclined at an angle \(30^{\circ}\) to the horizontal and allowed to fall. The angular velocity of the rod when it becomes horizontal is-
\(\left(\right.\) acceleration due to gravity \(=10 \mathbf{m s}^{-2}\) )

1 \(9 \mathrm{rad} \mathrm{s}^{-1}\)
2 \(6 \mathrm{rad} \mathrm{s}^{-1}\)
3 \(5 \mathrm{rad} \mathrm{s}^{-1}\)
4 \(8 \operatorname{rad~s}^{-1}\)
Rotational Motion

149776 A fan is rotating with an angular speed 300 rpm. The fan is switched off, and it takes \(80 \mathrm{~s}\) to come to rest. Assuming constant angular deceleration, the number of revolutions made by the fan before it comes to rest is

1 400
2 200
3 300
4 314
Rotational Motion

149778 A merry - go - round rotating at a constant angular speed completes 9 rotations in 18 seconds. What is it angular speed?

1 \(\pi / 2 \mathrm{rad} / \mathrm{s}\)
2 \(\pi \mathrm{rad} / \mathrm{s}\)
3 \(2 \pi \mathrm{rad} / \mathrm{s}\)
4 \(3 \pi \mathrm{rad} / \mathrm{s}\)
Rotational Motion

149779 A wheel moving with initial angular velocity 20 \(\mathrm{rad} / \mathrm{s}\), stops after 50 revolutions. The time taken by the wheel to stop is

1 \(17.1 \mathrm{sec}\)
2 \(15.7 \mathrm{sec}\)
3 \(31.4 \mathrm{sec}\)
4 \(47.1 \mathrm{sec}\)
Rotational Motion

149773 A thin circular ring of mass \(M\) and radius \(R\) rotates about an axis through its centre and perpendicular to its plane, with a constant angular velocity \(\omega\). Four small spheres each of mass \(m\) (negligible radius) are kept gently to the opposite ends of two mutually perpendicular diameters of the ring. The new angular velocity of the ring will be

1 \(4 \omega\)
2 \(\frac{M}{4 m} \omega\)
3 \(\left(\frac{M+4 m}{M}\right) \omega\)
4 \(\left(\frac{M}{M-4 m}\right) \omega\)
5 \(\left(\frac{M}{M+4 m}\right) \omega\)
Rotational Motion

149775 A uniform rod of length \(60 \mathrm{~cm}\) is placed with one end in contact with the horizontal table and is then inclined at an angle \(30^{\circ}\) to the horizontal and allowed to fall. The angular velocity of the rod when it becomes horizontal is-
\(\left(\right.\) acceleration due to gravity \(=10 \mathbf{m s}^{-2}\) )

1 \(9 \mathrm{rad} \mathrm{s}^{-1}\)
2 \(6 \mathrm{rad} \mathrm{s}^{-1}\)
3 \(5 \mathrm{rad} \mathrm{s}^{-1}\)
4 \(8 \operatorname{rad~s}^{-1}\)
Rotational Motion

149776 A fan is rotating with an angular speed 300 rpm. The fan is switched off, and it takes \(80 \mathrm{~s}\) to come to rest. Assuming constant angular deceleration, the number of revolutions made by the fan before it comes to rest is

1 400
2 200
3 300
4 314
Rotational Motion

149778 A merry - go - round rotating at a constant angular speed completes 9 rotations in 18 seconds. What is it angular speed?

1 \(\pi / 2 \mathrm{rad} / \mathrm{s}\)
2 \(\pi \mathrm{rad} / \mathrm{s}\)
3 \(2 \pi \mathrm{rad} / \mathrm{s}\)
4 \(3 \pi \mathrm{rad} / \mathrm{s}\)
Rotational Motion

149779 A wheel moving with initial angular velocity 20 \(\mathrm{rad} / \mathrm{s}\), stops after 50 revolutions. The time taken by the wheel to stop is

1 \(17.1 \mathrm{sec}\)
2 \(15.7 \mathrm{sec}\)
3 \(31.4 \mathrm{sec}\)
4 \(47.1 \mathrm{sec}\)
Rotational Motion

149773 A thin circular ring of mass \(M\) and radius \(R\) rotates about an axis through its centre and perpendicular to its plane, with a constant angular velocity \(\omega\). Four small spheres each of mass \(m\) (negligible radius) are kept gently to the opposite ends of two mutually perpendicular diameters of the ring. The new angular velocity of the ring will be

1 \(4 \omega\)
2 \(\frac{M}{4 m} \omega\)
3 \(\left(\frac{M+4 m}{M}\right) \omega\)
4 \(\left(\frac{M}{M-4 m}\right) \omega\)
5 \(\left(\frac{M}{M+4 m}\right) \omega\)
Rotational Motion

149775 A uniform rod of length \(60 \mathrm{~cm}\) is placed with one end in contact with the horizontal table and is then inclined at an angle \(30^{\circ}\) to the horizontal and allowed to fall. The angular velocity of the rod when it becomes horizontal is-
\(\left(\right.\) acceleration due to gravity \(=10 \mathbf{m s}^{-2}\) )

1 \(9 \mathrm{rad} \mathrm{s}^{-1}\)
2 \(6 \mathrm{rad} \mathrm{s}^{-1}\)
3 \(5 \mathrm{rad} \mathrm{s}^{-1}\)
4 \(8 \operatorname{rad~s}^{-1}\)
Rotational Motion

149776 A fan is rotating with an angular speed 300 rpm. The fan is switched off, and it takes \(80 \mathrm{~s}\) to come to rest. Assuming constant angular deceleration, the number of revolutions made by the fan before it comes to rest is

1 400
2 200
3 300
4 314
Rotational Motion

149778 A merry - go - round rotating at a constant angular speed completes 9 rotations in 18 seconds. What is it angular speed?

1 \(\pi / 2 \mathrm{rad} / \mathrm{s}\)
2 \(\pi \mathrm{rad} / \mathrm{s}\)
3 \(2 \pi \mathrm{rad} / \mathrm{s}\)
4 \(3 \pi \mathrm{rad} / \mathrm{s}\)
Rotational Motion

149779 A wheel moving with initial angular velocity 20 \(\mathrm{rad} / \mathrm{s}\), stops after 50 revolutions. The time taken by the wheel to stop is

1 \(17.1 \mathrm{sec}\)
2 \(15.7 \mathrm{sec}\)
3 \(31.4 \mathrm{sec}\)
4 \(47.1 \mathrm{sec}\)
Rotational Motion

149773 A thin circular ring of mass \(M\) and radius \(R\) rotates about an axis through its centre and perpendicular to its plane, with a constant angular velocity \(\omega\). Four small spheres each of mass \(m\) (negligible radius) are kept gently to the opposite ends of two mutually perpendicular diameters of the ring. The new angular velocity of the ring will be

1 \(4 \omega\)
2 \(\frac{M}{4 m} \omega\)
3 \(\left(\frac{M+4 m}{M}\right) \omega\)
4 \(\left(\frac{M}{M-4 m}\right) \omega\)
5 \(\left(\frac{M}{M+4 m}\right) \omega\)
Rotational Motion

149775 A uniform rod of length \(60 \mathrm{~cm}\) is placed with one end in contact with the horizontal table and is then inclined at an angle \(30^{\circ}\) to the horizontal and allowed to fall. The angular velocity of the rod when it becomes horizontal is-
\(\left(\right.\) acceleration due to gravity \(=10 \mathbf{m s}^{-2}\) )

1 \(9 \mathrm{rad} \mathrm{s}^{-1}\)
2 \(6 \mathrm{rad} \mathrm{s}^{-1}\)
3 \(5 \mathrm{rad} \mathrm{s}^{-1}\)
4 \(8 \operatorname{rad~s}^{-1}\)
Rotational Motion

149776 A fan is rotating with an angular speed 300 rpm. The fan is switched off, and it takes \(80 \mathrm{~s}\) to come to rest. Assuming constant angular deceleration, the number of revolutions made by the fan before it comes to rest is

1 400
2 200
3 300
4 314
Rotational Motion

149778 A merry - go - round rotating at a constant angular speed completes 9 rotations in 18 seconds. What is it angular speed?

1 \(\pi / 2 \mathrm{rad} / \mathrm{s}\)
2 \(\pi \mathrm{rad} / \mathrm{s}\)
3 \(2 \pi \mathrm{rad} / \mathrm{s}\)
4 \(3 \pi \mathrm{rad} / \mathrm{s}\)
Rotational Motion

149779 A wheel moving with initial angular velocity 20 \(\mathrm{rad} / \mathrm{s}\), stops after 50 revolutions. The time taken by the wheel to stop is

1 \(17.1 \mathrm{sec}\)
2 \(15.7 \mathrm{sec}\)
3 \(31.4 \mathrm{sec}\)
4 \(47.1 \mathrm{sec}\)
Rotational Motion

149773 A thin circular ring of mass \(M\) and radius \(R\) rotates about an axis through its centre and perpendicular to its plane, with a constant angular velocity \(\omega\). Four small spheres each of mass \(m\) (negligible radius) are kept gently to the opposite ends of two mutually perpendicular diameters of the ring. The new angular velocity of the ring will be

1 \(4 \omega\)
2 \(\frac{M}{4 m} \omega\)
3 \(\left(\frac{M+4 m}{M}\right) \omega\)
4 \(\left(\frac{M}{M-4 m}\right) \omega\)
5 \(\left(\frac{M}{M+4 m}\right) \omega\)
Rotational Motion

149775 A uniform rod of length \(60 \mathrm{~cm}\) is placed with one end in contact with the horizontal table and is then inclined at an angle \(30^{\circ}\) to the horizontal and allowed to fall. The angular velocity of the rod when it becomes horizontal is-
\(\left(\right.\) acceleration due to gravity \(=10 \mathbf{m s}^{-2}\) )

1 \(9 \mathrm{rad} \mathrm{s}^{-1}\)
2 \(6 \mathrm{rad} \mathrm{s}^{-1}\)
3 \(5 \mathrm{rad} \mathrm{s}^{-1}\)
4 \(8 \operatorname{rad~s}^{-1}\)
Rotational Motion

149776 A fan is rotating with an angular speed 300 rpm. The fan is switched off, and it takes \(80 \mathrm{~s}\) to come to rest. Assuming constant angular deceleration, the number of revolutions made by the fan before it comes to rest is

1 400
2 200
3 300
4 314
Rotational Motion

149778 A merry - go - round rotating at a constant angular speed completes 9 rotations in 18 seconds. What is it angular speed?

1 \(\pi / 2 \mathrm{rad} / \mathrm{s}\)
2 \(\pi \mathrm{rad} / \mathrm{s}\)
3 \(2 \pi \mathrm{rad} / \mathrm{s}\)
4 \(3 \pi \mathrm{rad} / \mathrm{s}\)
Rotational Motion

149779 A wheel moving with initial angular velocity 20 \(\mathrm{rad} / \mathrm{s}\), stops after 50 revolutions. The time taken by the wheel to stop is

1 \(17.1 \mathrm{sec}\)
2 \(15.7 \mathrm{sec}\)
3 \(31.4 \mathrm{sec}\)
4 \(47.1 \mathrm{sec}\)