06. Rolling Motion
Rotational Motion

150421 A solid sphere of mass \(5 \mathrm{~kg}\) rolls on a plane surface. Find its kinetic energy at an instant when its centre moves with speed \(4 \mathrm{~m} / \mathrm{s}\).

1 \(56 \mathrm{~J}\)
2 \(45 \mathrm{~J}\)
3 \(75 \mathrm{~J}\)
4 \(105 \mathrm{~J}\)
Rotational Motion

150422 Three bodies, a ring, a solid disc and a solid sphere roll down the same inclined plane without slipping. The radii of the bodies are identical and they start from rest. If \(V_{s}, V_{R}\) and \(V_{D}\) are the speeds of the sphere, ring and disc, respectively when they reach the bottom, then the correct option is

1 \(V_{s}>V_{R}>V_{D}\)
2 \(\mathrm{V}_{\mathrm{D}}>\mathrm{V}_{\mathrm{S}}>\mathrm{V}_{\mathrm{R}}\)
3 \(V_{R}>V_{D}>V_{S}\)
4 \(V_{S}>V_{D}>V_{R}\)
Rotational Motion

150423 A solid sphere rolls down without slipping on a smooth inclined plane of inclination \(\sin ^{-1}(0.42\). If the acceleration due to gravity is \(10 \mathrm{~ms}^{-2}\), the acceleration of the rolling sphere is

1 \(1 \mathrm{~ms}^{-2}\)
2 \(2 \mathrm{~ms}^{-2}\)
3 \(3 \mathrm{~ms}^{-2}\)
4 \(4 \mathrm{~ms}^{-2}\)
Rotational Motion

150424 A tangential force \(F\) acts at the top of a thin spherical shell of mass \(m\) and radius \(R\). The acceleration of the shell if it rolls without slipping is ( \(f=\) rolling friction)

1 \(\frac{5 \mathrm{~F}}{6 \mathrm{~m}}\)
2 \(\frac{6 \mathrm{~F}}{5 \mathrm{~m}}\)
3 \(\frac{3 \mathrm{~F}}{2 \mathrm{~m}}\)
4 \(\frac{F}{6 \mathrm{~m}}\)
Rotational Motion

150425 A solid sphere is in rolling motion. In rolling motion, a body possesses translational kinetic energy \(\left(K_{t}\right)\) as well as rotational kinetic energy \(\left(K_{r}\right)\) simultaneously. The ratio \(K_{t}:\left(K_{t}+K_{r}\right)\) for the sphere is

1 \(10: 7\)
2 \(5: 7\)
3 \(7: 10\)
4 \(2: 5\)
Rotational Motion

150421 A solid sphere of mass \(5 \mathrm{~kg}\) rolls on a plane surface. Find its kinetic energy at an instant when its centre moves with speed \(4 \mathrm{~m} / \mathrm{s}\).

1 \(56 \mathrm{~J}\)
2 \(45 \mathrm{~J}\)
3 \(75 \mathrm{~J}\)
4 \(105 \mathrm{~J}\)
Rotational Motion

150422 Three bodies, a ring, a solid disc and a solid sphere roll down the same inclined plane without slipping. The radii of the bodies are identical and they start from rest. If \(V_{s}, V_{R}\) and \(V_{D}\) are the speeds of the sphere, ring and disc, respectively when they reach the bottom, then the correct option is

1 \(V_{s}>V_{R}>V_{D}\)
2 \(\mathrm{V}_{\mathrm{D}}>\mathrm{V}_{\mathrm{S}}>\mathrm{V}_{\mathrm{R}}\)
3 \(V_{R}>V_{D}>V_{S}\)
4 \(V_{S}>V_{D}>V_{R}\)
Rotational Motion

150423 A solid sphere rolls down without slipping on a smooth inclined plane of inclination \(\sin ^{-1}(0.42\). If the acceleration due to gravity is \(10 \mathrm{~ms}^{-2}\), the acceleration of the rolling sphere is

1 \(1 \mathrm{~ms}^{-2}\)
2 \(2 \mathrm{~ms}^{-2}\)
3 \(3 \mathrm{~ms}^{-2}\)
4 \(4 \mathrm{~ms}^{-2}\)
Rotational Motion

150424 A tangential force \(F\) acts at the top of a thin spherical shell of mass \(m\) and radius \(R\). The acceleration of the shell if it rolls without slipping is ( \(f=\) rolling friction)

1 \(\frac{5 \mathrm{~F}}{6 \mathrm{~m}}\)
2 \(\frac{6 \mathrm{~F}}{5 \mathrm{~m}}\)
3 \(\frac{3 \mathrm{~F}}{2 \mathrm{~m}}\)
4 \(\frac{F}{6 \mathrm{~m}}\)
Rotational Motion

150425 A solid sphere is in rolling motion. In rolling motion, a body possesses translational kinetic energy \(\left(K_{t}\right)\) as well as rotational kinetic energy \(\left(K_{r}\right)\) simultaneously. The ratio \(K_{t}:\left(K_{t}+K_{r}\right)\) for the sphere is

1 \(10: 7\)
2 \(5: 7\)
3 \(7: 10\)
4 \(2: 5\)
Rotational Motion

150421 A solid sphere of mass \(5 \mathrm{~kg}\) rolls on a plane surface. Find its kinetic energy at an instant when its centre moves with speed \(4 \mathrm{~m} / \mathrm{s}\).

1 \(56 \mathrm{~J}\)
2 \(45 \mathrm{~J}\)
3 \(75 \mathrm{~J}\)
4 \(105 \mathrm{~J}\)
Rotational Motion

150422 Three bodies, a ring, a solid disc and a solid sphere roll down the same inclined plane without slipping. The radii of the bodies are identical and they start from rest. If \(V_{s}, V_{R}\) and \(V_{D}\) are the speeds of the sphere, ring and disc, respectively when they reach the bottom, then the correct option is

1 \(V_{s}>V_{R}>V_{D}\)
2 \(\mathrm{V}_{\mathrm{D}}>\mathrm{V}_{\mathrm{S}}>\mathrm{V}_{\mathrm{R}}\)
3 \(V_{R}>V_{D}>V_{S}\)
4 \(V_{S}>V_{D}>V_{R}\)
Rotational Motion

150423 A solid sphere rolls down without slipping on a smooth inclined plane of inclination \(\sin ^{-1}(0.42\). If the acceleration due to gravity is \(10 \mathrm{~ms}^{-2}\), the acceleration of the rolling sphere is

1 \(1 \mathrm{~ms}^{-2}\)
2 \(2 \mathrm{~ms}^{-2}\)
3 \(3 \mathrm{~ms}^{-2}\)
4 \(4 \mathrm{~ms}^{-2}\)
Rotational Motion

150424 A tangential force \(F\) acts at the top of a thin spherical shell of mass \(m\) and radius \(R\). The acceleration of the shell if it rolls without slipping is ( \(f=\) rolling friction)

1 \(\frac{5 \mathrm{~F}}{6 \mathrm{~m}}\)
2 \(\frac{6 \mathrm{~F}}{5 \mathrm{~m}}\)
3 \(\frac{3 \mathrm{~F}}{2 \mathrm{~m}}\)
4 \(\frac{F}{6 \mathrm{~m}}\)
Rotational Motion

150425 A solid sphere is in rolling motion. In rolling motion, a body possesses translational kinetic energy \(\left(K_{t}\right)\) as well as rotational kinetic energy \(\left(K_{r}\right)\) simultaneously. The ratio \(K_{t}:\left(K_{t}+K_{r}\right)\) for the sphere is

1 \(10: 7\)
2 \(5: 7\)
3 \(7: 10\)
4 \(2: 5\)
Rotational Motion

150421 A solid sphere of mass \(5 \mathrm{~kg}\) rolls on a plane surface. Find its kinetic energy at an instant when its centre moves with speed \(4 \mathrm{~m} / \mathrm{s}\).

1 \(56 \mathrm{~J}\)
2 \(45 \mathrm{~J}\)
3 \(75 \mathrm{~J}\)
4 \(105 \mathrm{~J}\)
Rotational Motion

150422 Three bodies, a ring, a solid disc and a solid sphere roll down the same inclined plane without slipping. The radii of the bodies are identical and they start from rest. If \(V_{s}, V_{R}\) and \(V_{D}\) are the speeds of the sphere, ring and disc, respectively when they reach the bottom, then the correct option is

1 \(V_{s}>V_{R}>V_{D}\)
2 \(\mathrm{V}_{\mathrm{D}}>\mathrm{V}_{\mathrm{S}}>\mathrm{V}_{\mathrm{R}}\)
3 \(V_{R}>V_{D}>V_{S}\)
4 \(V_{S}>V_{D}>V_{R}\)
Rotational Motion

150423 A solid sphere rolls down without slipping on a smooth inclined plane of inclination \(\sin ^{-1}(0.42\). If the acceleration due to gravity is \(10 \mathrm{~ms}^{-2}\), the acceleration of the rolling sphere is

1 \(1 \mathrm{~ms}^{-2}\)
2 \(2 \mathrm{~ms}^{-2}\)
3 \(3 \mathrm{~ms}^{-2}\)
4 \(4 \mathrm{~ms}^{-2}\)
Rotational Motion

150424 A tangential force \(F\) acts at the top of a thin spherical shell of mass \(m\) and radius \(R\). The acceleration of the shell if it rolls without slipping is ( \(f=\) rolling friction)

1 \(\frac{5 \mathrm{~F}}{6 \mathrm{~m}}\)
2 \(\frac{6 \mathrm{~F}}{5 \mathrm{~m}}\)
3 \(\frac{3 \mathrm{~F}}{2 \mathrm{~m}}\)
4 \(\frac{F}{6 \mathrm{~m}}\)
Rotational Motion

150425 A solid sphere is in rolling motion. In rolling motion, a body possesses translational kinetic energy \(\left(K_{t}\right)\) as well as rotational kinetic energy \(\left(K_{r}\right)\) simultaneously. The ratio \(K_{t}:\left(K_{t}+K_{r}\right)\) for the sphere is

1 \(10: 7\)
2 \(5: 7\)
3 \(7: 10\)
4 \(2: 5\)
Rotational Motion

150421 A solid sphere of mass \(5 \mathrm{~kg}\) rolls on a plane surface. Find its kinetic energy at an instant when its centre moves with speed \(4 \mathrm{~m} / \mathrm{s}\).

1 \(56 \mathrm{~J}\)
2 \(45 \mathrm{~J}\)
3 \(75 \mathrm{~J}\)
4 \(105 \mathrm{~J}\)
Rotational Motion

150422 Three bodies, a ring, a solid disc and a solid sphere roll down the same inclined plane without slipping. The radii of the bodies are identical and they start from rest. If \(V_{s}, V_{R}\) and \(V_{D}\) are the speeds of the sphere, ring and disc, respectively when they reach the bottom, then the correct option is

1 \(V_{s}>V_{R}>V_{D}\)
2 \(\mathrm{V}_{\mathrm{D}}>\mathrm{V}_{\mathrm{S}}>\mathrm{V}_{\mathrm{R}}\)
3 \(V_{R}>V_{D}>V_{S}\)
4 \(V_{S}>V_{D}>V_{R}\)
Rotational Motion

150423 A solid sphere rolls down without slipping on a smooth inclined plane of inclination \(\sin ^{-1}(0.42\). If the acceleration due to gravity is \(10 \mathrm{~ms}^{-2}\), the acceleration of the rolling sphere is

1 \(1 \mathrm{~ms}^{-2}\)
2 \(2 \mathrm{~ms}^{-2}\)
3 \(3 \mathrm{~ms}^{-2}\)
4 \(4 \mathrm{~ms}^{-2}\)
Rotational Motion

150424 A tangential force \(F\) acts at the top of a thin spherical shell of mass \(m\) and radius \(R\). The acceleration of the shell if it rolls without slipping is ( \(f=\) rolling friction)

1 \(\frac{5 \mathrm{~F}}{6 \mathrm{~m}}\)
2 \(\frac{6 \mathrm{~F}}{5 \mathrm{~m}}\)
3 \(\frac{3 \mathrm{~F}}{2 \mathrm{~m}}\)
4 \(\frac{F}{6 \mathrm{~m}}\)
Rotational Motion

150425 A solid sphere is in rolling motion. In rolling motion, a body possesses translational kinetic energy \(\left(K_{t}\right)\) as well as rotational kinetic energy \(\left(K_{r}\right)\) simultaneously. The ratio \(K_{t}:\left(K_{t}+K_{r}\right)\) for the sphere is

1 \(10: 7\)
2 \(5: 7\)
3 \(7: 10\)
4 \(2: 5\)