02. Torque, Angular Momentum
Rotational Motion

149931 Two flywheels \(A\) and \(B\) are mounted side by side with frictionless bearings on a common shaft. Their moments of inertia about the shaft are \(5.0 \mathrm{~kg}-\mathrm{m}^{2}\) and \(20.0 \mathrm{~kg}-\mathrm{m}^{2}\) respectively. Wheel \(A\) is made to rotate at 10 revolution per second. Wheel \(B\), initially stationary, is now coupled to \(A\) with the help of a clutch. The rotation speed of the wheels will become

1 \(2 \sqrt{5} \mathrm{rps}\)
2 \(0.5 \mathrm{rps}\)
3 \(2 \mathrm{rps}\)
4 \(3 \mathrm{rps}\)
Rotational Motion

149932 A circular hoop of radius \(50 \mathrm{~cm}\) and mass \(1 \mathrm{~kg}\) rotating with an angular velocity \(\omega_{0}\) is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. Let ' \(v\) ' be the velocity of the centre of the hoop when it ceases to slip. The ratio \(\mathrm{v} / \omega_{0}\) will be:

1 \(10 \mathrm{~cm}\)
2 \(50 \mathrm{~cm}\)
3 \(25 \mathrm{~cm}\)
4 \(12.5 \mathrm{~cm}\)
Rotational Motion

149933 A mass \(m\) is supported by a massless string wound around a uniform cylinder of mass \(\mathrm{m}\) and radius \(R\). On releasing the mass from rest, it will fall with acceleration

1 \(g\)
2 \(\frac{g}{2}\)
3 \(\frac{2 g}{3}\)
4 \(\frac{3 g}{2}\)
Rotational Motion

149934 A same torque is applied to a disc and a ring of equal mass and radii then

1 both will rotate with same angular acceleration.
2 the ring will rotate with greater angular acceleration.
3 both will rotate with same angular velocity.
4 the disc will rotate with greater angular frequency.
Rotational Motion

149936 A solid sphere of radius \(r\) is revolving about one of its diameters with an angular velocity \(\omega\). If it suddenly expands uniformly so that its radius increases to \(\mathrm{n}\) times its original value, then its angular velocity becomes

1 \(n^{2} \omega\)
2 \(\frac{\omega}{\mathrm{n}^{2}}\)
3 \(\mathrm{n} \omega\)
4 \(\frac{\omega}{\mathrm{n}}\)
5 \(2 \mathrm{n} \omega\)
Rotational Motion

149931 Two flywheels \(A\) and \(B\) are mounted side by side with frictionless bearings on a common shaft. Their moments of inertia about the shaft are \(5.0 \mathrm{~kg}-\mathrm{m}^{2}\) and \(20.0 \mathrm{~kg}-\mathrm{m}^{2}\) respectively. Wheel \(A\) is made to rotate at 10 revolution per second. Wheel \(B\), initially stationary, is now coupled to \(A\) with the help of a clutch. The rotation speed of the wheels will become

1 \(2 \sqrt{5} \mathrm{rps}\)
2 \(0.5 \mathrm{rps}\)
3 \(2 \mathrm{rps}\)
4 \(3 \mathrm{rps}\)
Rotational Motion

149932 A circular hoop of radius \(50 \mathrm{~cm}\) and mass \(1 \mathrm{~kg}\) rotating with an angular velocity \(\omega_{0}\) is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. Let ' \(v\) ' be the velocity of the centre of the hoop when it ceases to slip. The ratio \(\mathrm{v} / \omega_{0}\) will be:

1 \(10 \mathrm{~cm}\)
2 \(50 \mathrm{~cm}\)
3 \(25 \mathrm{~cm}\)
4 \(12.5 \mathrm{~cm}\)
Rotational Motion

149933 A mass \(m\) is supported by a massless string wound around a uniform cylinder of mass \(\mathrm{m}\) and radius \(R\). On releasing the mass from rest, it will fall with acceleration

1 \(g\)
2 \(\frac{g}{2}\)
3 \(\frac{2 g}{3}\)
4 \(\frac{3 g}{2}\)
Rotational Motion

149934 A same torque is applied to a disc and a ring of equal mass and radii then

1 both will rotate with same angular acceleration.
2 the ring will rotate with greater angular acceleration.
3 both will rotate with same angular velocity.
4 the disc will rotate with greater angular frequency.
Rotational Motion

149936 A solid sphere of radius \(r\) is revolving about one of its diameters with an angular velocity \(\omega\). If it suddenly expands uniformly so that its radius increases to \(\mathrm{n}\) times its original value, then its angular velocity becomes

1 \(n^{2} \omega\)
2 \(\frac{\omega}{\mathrm{n}^{2}}\)
3 \(\mathrm{n} \omega\)
4 \(\frac{\omega}{\mathrm{n}}\)
5 \(2 \mathrm{n} \omega\)
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Rotational Motion

149931 Two flywheels \(A\) and \(B\) are mounted side by side with frictionless bearings on a common shaft. Their moments of inertia about the shaft are \(5.0 \mathrm{~kg}-\mathrm{m}^{2}\) and \(20.0 \mathrm{~kg}-\mathrm{m}^{2}\) respectively. Wheel \(A\) is made to rotate at 10 revolution per second. Wheel \(B\), initially stationary, is now coupled to \(A\) with the help of a clutch. The rotation speed of the wheels will become

1 \(2 \sqrt{5} \mathrm{rps}\)
2 \(0.5 \mathrm{rps}\)
3 \(2 \mathrm{rps}\)
4 \(3 \mathrm{rps}\)
Rotational Motion

149932 A circular hoop of radius \(50 \mathrm{~cm}\) and mass \(1 \mathrm{~kg}\) rotating with an angular velocity \(\omega_{0}\) is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. Let ' \(v\) ' be the velocity of the centre of the hoop when it ceases to slip. The ratio \(\mathrm{v} / \omega_{0}\) will be:

1 \(10 \mathrm{~cm}\)
2 \(50 \mathrm{~cm}\)
3 \(25 \mathrm{~cm}\)
4 \(12.5 \mathrm{~cm}\)
Rotational Motion

149933 A mass \(m\) is supported by a massless string wound around a uniform cylinder of mass \(\mathrm{m}\) and radius \(R\). On releasing the mass from rest, it will fall with acceleration

1 \(g\)
2 \(\frac{g}{2}\)
3 \(\frac{2 g}{3}\)
4 \(\frac{3 g}{2}\)
Rotational Motion

149934 A same torque is applied to a disc and a ring of equal mass and radii then

1 both will rotate with same angular acceleration.
2 the ring will rotate with greater angular acceleration.
3 both will rotate with same angular velocity.
4 the disc will rotate with greater angular frequency.
Rotational Motion

149936 A solid sphere of radius \(r\) is revolving about one of its diameters with an angular velocity \(\omega\). If it suddenly expands uniformly so that its radius increases to \(\mathrm{n}\) times its original value, then its angular velocity becomes

1 \(n^{2} \omega\)
2 \(\frac{\omega}{\mathrm{n}^{2}}\)
3 \(\mathrm{n} \omega\)
4 \(\frac{\omega}{\mathrm{n}}\)
5 \(2 \mathrm{n} \omega\)
Rotational Motion

149931 Two flywheels \(A\) and \(B\) are mounted side by side with frictionless bearings on a common shaft. Their moments of inertia about the shaft are \(5.0 \mathrm{~kg}-\mathrm{m}^{2}\) and \(20.0 \mathrm{~kg}-\mathrm{m}^{2}\) respectively. Wheel \(A\) is made to rotate at 10 revolution per second. Wheel \(B\), initially stationary, is now coupled to \(A\) with the help of a clutch. The rotation speed of the wheels will become

1 \(2 \sqrt{5} \mathrm{rps}\)
2 \(0.5 \mathrm{rps}\)
3 \(2 \mathrm{rps}\)
4 \(3 \mathrm{rps}\)
Rotational Motion

149932 A circular hoop of radius \(50 \mathrm{~cm}\) and mass \(1 \mathrm{~kg}\) rotating with an angular velocity \(\omega_{0}\) is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. Let ' \(v\) ' be the velocity of the centre of the hoop when it ceases to slip. The ratio \(\mathrm{v} / \omega_{0}\) will be:

1 \(10 \mathrm{~cm}\)
2 \(50 \mathrm{~cm}\)
3 \(25 \mathrm{~cm}\)
4 \(12.5 \mathrm{~cm}\)
Rotational Motion

149933 A mass \(m\) is supported by a massless string wound around a uniform cylinder of mass \(\mathrm{m}\) and radius \(R\). On releasing the mass from rest, it will fall with acceleration

1 \(g\)
2 \(\frac{g}{2}\)
3 \(\frac{2 g}{3}\)
4 \(\frac{3 g}{2}\)
Rotational Motion

149934 A same torque is applied to a disc and a ring of equal mass and radii then

1 both will rotate with same angular acceleration.
2 the ring will rotate with greater angular acceleration.
3 both will rotate with same angular velocity.
4 the disc will rotate with greater angular frequency.
Rotational Motion

149936 A solid sphere of radius \(r\) is revolving about one of its diameters with an angular velocity \(\omega\). If it suddenly expands uniformly so that its radius increases to \(\mathrm{n}\) times its original value, then its angular velocity becomes

1 \(n^{2} \omega\)
2 \(\frac{\omega}{\mathrm{n}^{2}}\)
3 \(\mathrm{n} \omega\)
4 \(\frac{\omega}{\mathrm{n}}\)
5 \(2 \mathrm{n} \omega\)
Rotational Motion

149931 Two flywheels \(A\) and \(B\) are mounted side by side with frictionless bearings on a common shaft. Their moments of inertia about the shaft are \(5.0 \mathrm{~kg}-\mathrm{m}^{2}\) and \(20.0 \mathrm{~kg}-\mathrm{m}^{2}\) respectively. Wheel \(A\) is made to rotate at 10 revolution per second. Wheel \(B\), initially stationary, is now coupled to \(A\) with the help of a clutch. The rotation speed of the wheels will become

1 \(2 \sqrt{5} \mathrm{rps}\)
2 \(0.5 \mathrm{rps}\)
3 \(2 \mathrm{rps}\)
4 \(3 \mathrm{rps}\)
Rotational Motion

149932 A circular hoop of radius \(50 \mathrm{~cm}\) and mass \(1 \mathrm{~kg}\) rotating with an angular velocity \(\omega_{0}\) is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. Let ' \(v\) ' be the velocity of the centre of the hoop when it ceases to slip. The ratio \(\mathrm{v} / \omega_{0}\) will be:

1 \(10 \mathrm{~cm}\)
2 \(50 \mathrm{~cm}\)
3 \(25 \mathrm{~cm}\)
4 \(12.5 \mathrm{~cm}\)
Rotational Motion

149933 A mass \(m\) is supported by a massless string wound around a uniform cylinder of mass \(\mathrm{m}\) and radius \(R\). On releasing the mass from rest, it will fall with acceleration

1 \(g\)
2 \(\frac{g}{2}\)
3 \(\frac{2 g}{3}\)
4 \(\frac{3 g}{2}\)
Rotational Motion

149934 A same torque is applied to a disc and a ring of equal mass and radii then

1 both will rotate with same angular acceleration.
2 the ring will rotate with greater angular acceleration.
3 both will rotate with same angular velocity.
4 the disc will rotate with greater angular frequency.
Rotational Motion

149936 A solid sphere of radius \(r\) is revolving about one of its diameters with an angular velocity \(\omega\). If it suddenly expands uniformly so that its radius increases to \(\mathrm{n}\) times its original value, then its angular velocity becomes

1 \(n^{2} \omega\)
2 \(\frac{\omega}{\mathrm{n}^{2}}\)
3 \(\mathrm{n} \omega\)
4 \(\frac{\omega}{\mathrm{n}}\)
5 \(2 \mathrm{n} \omega\)