06. Rolling Motion
Rotational Motion

150459 Three bodies a ring (R), a solid cylinder (C) and a solid sphere ( \(S\)having same mass and same radius roll down the inclined plane without slipping. They start from rest, if \(v_{R}, v_{C}\) and \(v_{S}\) are velocities of respective bodies on reaching the bottom of the plane, then :

1 \(v_{\mathrm{R}}=v_{\mathrm{C}}=v_{\mathrm{S}}\)
2 \(v_{R}>v_{C}>v_{S}\)
3 \(v_{\mathrm{R}} \lt v_{\mathrm{C}} \lt v_{\mathrm{S}}\)
4 \(v_{\mathrm{R}}=v_{\mathrm{C}}>v_{\mathrm{S}}\)
Rotational Motion

150460 A ring starts to roll down the inclined plane of height \(h\) without slipping. The velocity with which it reaches the ground is

1 \(\sqrt{\frac{10 \mathrm{gh}}{7}}\)
2 \(\sqrt{\frac{4 \mathrm{gh}}{7}}\)
3 \(\sqrt{\frac{4 \mathrm{gh}}{3}}\)
4 \(\sqrt{2 \text { gh }}\)
5 \(\sqrt{\mathrm{gh}}\)
Rotational Motion

150461 A solid sphere of mass \(2 \mathrm{~kg}\) rolls on a smooth horizontal surface at \(10 \mathrm{~m} / \mathrm{s}\) and then rolls up a smooth \(3^{\circ}\) incline. The maximum height reached by the sphere is \(\left(g=9.8 \mathrm{~m} / \mathrm{s}^{2}\right)\)

1 \(10 \mathrm{~m}\)
2 \(4.9 \mathrm{~m}\)
3 \(14.2 \mathrm{~m}\)
4 \(7.1 \mathrm{~m}\)
Rotational Motion

150462 The acceleration of the centre of mass of a uniform solid disc rolling down an inclined plane of angle \(\alpha\) is

1 \(g \sin \alpha\)
2 \(2 / 3 g \sin \alpha\)
3 \(1 / 2 \mathrm{~g} \sin \alpha\)
4 \(1 / 3 \mathrm{~g} \sin \alpha\)
Rotational Motion

150463 A solid sphere of mass \(1 \mathrm{~kg}\), radius \(10 \mathrm{~cm}\) rolls down an inclined plane of height \(7 \mathrm{~m}\). The velocity of its centre as it reaches the ground level is

1 \(7 \mathrm{~m} / \mathrm{s}\)
2 \(10 \mathrm{~m} / \mathrm{s}\)
3 \(15 \mathrm{~m} / \mathrm{s}\)
4 \(20 \mathrm{~m} / \mathrm{s}\)
Rotational Motion

150459 Three bodies a ring (R), a solid cylinder (C) and a solid sphere ( \(S\)having same mass and same radius roll down the inclined plane without slipping. They start from rest, if \(v_{R}, v_{C}\) and \(v_{S}\) are velocities of respective bodies on reaching the bottom of the plane, then :

1 \(v_{\mathrm{R}}=v_{\mathrm{C}}=v_{\mathrm{S}}\)
2 \(v_{R}>v_{C}>v_{S}\)
3 \(v_{\mathrm{R}} \lt v_{\mathrm{C}} \lt v_{\mathrm{S}}\)
4 \(v_{\mathrm{R}}=v_{\mathrm{C}}>v_{\mathrm{S}}\)
Rotational Motion

150460 A ring starts to roll down the inclined plane of height \(h\) without slipping. The velocity with which it reaches the ground is

1 \(\sqrt{\frac{10 \mathrm{gh}}{7}}\)
2 \(\sqrt{\frac{4 \mathrm{gh}}{7}}\)
3 \(\sqrt{\frac{4 \mathrm{gh}}{3}}\)
4 \(\sqrt{2 \text { gh }}\)
5 \(\sqrt{\mathrm{gh}}\)
Rotational Motion

150461 A solid sphere of mass \(2 \mathrm{~kg}\) rolls on a smooth horizontal surface at \(10 \mathrm{~m} / \mathrm{s}\) and then rolls up a smooth \(3^{\circ}\) incline. The maximum height reached by the sphere is \(\left(g=9.8 \mathrm{~m} / \mathrm{s}^{2}\right)\)

1 \(10 \mathrm{~m}\)
2 \(4.9 \mathrm{~m}\)
3 \(14.2 \mathrm{~m}\)
4 \(7.1 \mathrm{~m}\)
Rotational Motion

150462 The acceleration of the centre of mass of a uniform solid disc rolling down an inclined plane of angle \(\alpha\) is

1 \(g \sin \alpha\)
2 \(2 / 3 g \sin \alpha\)
3 \(1 / 2 \mathrm{~g} \sin \alpha\)
4 \(1 / 3 \mathrm{~g} \sin \alpha\)
Rotational Motion

150463 A solid sphere of mass \(1 \mathrm{~kg}\), radius \(10 \mathrm{~cm}\) rolls down an inclined plane of height \(7 \mathrm{~m}\). The velocity of its centre as it reaches the ground level is

1 \(7 \mathrm{~m} / \mathrm{s}\)
2 \(10 \mathrm{~m} / \mathrm{s}\)
3 \(15 \mathrm{~m} / \mathrm{s}\)
4 \(20 \mathrm{~m} / \mathrm{s}\)
Rotational Motion

150459 Three bodies a ring (R), a solid cylinder (C) and a solid sphere ( \(S\)having same mass and same radius roll down the inclined plane without slipping. They start from rest, if \(v_{R}, v_{C}\) and \(v_{S}\) are velocities of respective bodies on reaching the bottom of the plane, then :

1 \(v_{\mathrm{R}}=v_{\mathrm{C}}=v_{\mathrm{S}}\)
2 \(v_{R}>v_{C}>v_{S}\)
3 \(v_{\mathrm{R}} \lt v_{\mathrm{C}} \lt v_{\mathrm{S}}\)
4 \(v_{\mathrm{R}}=v_{\mathrm{C}}>v_{\mathrm{S}}\)
Rotational Motion

150460 A ring starts to roll down the inclined plane of height \(h\) without slipping. The velocity with which it reaches the ground is

1 \(\sqrt{\frac{10 \mathrm{gh}}{7}}\)
2 \(\sqrt{\frac{4 \mathrm{gh}}{7}}\)
3 \(\sqrt{\frac{4 \mathrm{gh}}{3}}\)
4 \(\sqrt{2 \text { gh }}\)
5 \(\sqrt{\mathrm{gh}}\)
Rotational Motion

150461 A solid sphere of mass \(2 \mathrm{~kg}\) rolls on a smooth horizontal surface at \(10 \mathrm{~m} / \mathrm{s}\) and then rolls up a smooth \(3^{\circ}\) incline. The maximum height reached by the sphere is \(\left(g=9.8 \mathrm{~m} / \mathrm{s}^{2}\right)\)

1 \(10 \mathrm{~m}\)
2 \(4.9 \mathrm{~m}\)
3 \(14.2 \mathrm{~m}\)
4 \(7.1 \mathrm{~m}\)
Rotational Motion

150462 The acceleration of the centre of mass of a uniform solid disc rolling down an inclined plane of angle \(\alpha\) is

1 \(g \sin \alpha\)
2 \(2 / 3 g \sin \alpha\)
3 \(1 / 2 \mathrm{~g} \sin \alpha\)
4 \(1 / 3 \mathrm{~g} \sin \alpha\)
Rotational Motion

150463 A solid sphere of mass \(1 \mathrm{~kg}\), radius \(10 \mathrm{~cm}\) rolls down an inclined plane of height \(7 \mathrm{~m}\). The velocity of its centre as it reaches the ground level is

1 \(7 \mathrm{~m} / \mathrm{s}\)
2 \(10 \mathrm{~m} / \mathrm{s}\)
3 \(15 \mathrm{~m} / \mathrm{s}\)
4 \(20 \mathrm{~m} / \mathrm{s}\)
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Rotational Motion

150459 Three bodies a ring (R), a solid cylinder (C) and a solid sphere ( \(S\)having same mass and same radius roll down the inclined plane without slipping. They start from rest, if \(v_{R}, v_{C}\) and \(v_{S}\) are velocities of respective bodies on reaching the bottom of the plane, then :

1 \(v_{\mathrm{R}}=v_{\mathrm{C}}=v_{\mathrm{S}}\)
2 \(v_{R}>v_{C}>v_{S}\)
3 \(v_{\mathrm{R}} \lt v_{\mathrm{C}} \lt v_{\mathrm{S}}\)
4 \(v_{\mathrm{R}}=v_{\mathrm{C}}>v_{\mathrm{S}}\)
Rotational Motion

150460 A ring starts to roll down the inclined plane of height \(h\) without slipping. The velocity with which it reaches the ground is

1 \(\sqrt{\frac{10 \mathrm{gh}}{7}}\)
2 \(\sqrt{\frac{4 \mathrm{gh}}{7}}\)
3 \(\sqrt{\frac{4 \mathrm{gh}}{3}}\)
4 \(\sqrt{2 \text { gh }}\)
5 \(\sqrt{\mathrm{gh}}\)
Rotational Motion

150461 A solid sphere of mass \(2 \mathrm{~kg}\) rolls on a smooth horizontal surface at \(10 \mathrm{~m} / \mathrm{s}\) and then rolls up a smooth \(3^{\circ}\) incline. The maximum height reached by the sphere is \(\left(g=9.8 \mathrm{~m} / \mathrm{s}^{2}\right)\)

1 \(10 \mathrm{~m}\)
2 \(4.9 \mathrm{~m}\)
3 \(14.2 \mathrm{~m}\)
4 \(7.1 \mathrm{~m}\)
Rotational Motion

150462 The acceleration of the centre of mass of a uniform solid disc rolling down an inclined plane of angle \(\alpha\) is

1 \(g \sin \alpha\)
2 \(2 / 3 g \sin \alpha\)
3 \(1 / 2 \mathrm{~g} \sin \alpha\)
4 \(1 / 3 \mathrm{~g} \sin \alpha\)
Rotational Motion

150463 A solid sphere of mass \(1 \mathrm{~kg}\), radius \(10 \mathrm{~cm}\) rolls down an inclined plane of height \(7 \mathrm{~m}\). The velocity of its centre as it reaches the ground level is

1 \(7 \mathrm{~m} / \mathrm{s}\)
2 \(10 \mathrm{~m} / \mathrm{s}\)
3 \(15 \mathrm{~m} / \mathrm{s}\)
4 \(20 \mathrm{~m} / \mathrm{s}\)
Rotational Motion

150459 Three bodies a ring (R), a solid cylinder (C) and a solid sphere ( \(S\)having same mass and same radius roll down the inclined plane without slipping. They start from rest, if \(v_{R}, v_{C}\) and \(v_{S}\) are velocities of respective bodies on reaching the bottom of the plane, then :

1 \(v_{\mathrm{R}}=v_{\mathrm{C}}=v_{\mathrm{S}}\)
2 \(v_{R}>v_{C}>v_{S}\)
3 \(v_{\mathrm{R}} \lt v_{\mathrm{C}} \lt v_{\mathrm{S}}\)
4 \(v_{\mathrm{R}}=v_{\mathrm{C}}>v_{\mathrm{S}}\)
Rotational Motion

150460 A ring starts to roll down the inclined plane of height \(h\) without slipping. The velocity with which it reaches the ground is

1 \(\sqrt{\frac{10 \mathrm{gh}}{7}}\)
2 \(\sqrt{\frac{4 \mathrm{gh}}{7}}\)
3 \(\sqrt{\frac{4 \mathrm{gh}}{3}}\)
4 \(\sqrt{2 \text { gh }}\)
5 \(\sqrt{\mathrm{gh}}\)
Rotational Motion

150461 A solid sphere of mass \(2 \mathrm{~kg}\) rolls on a smooth horizontal surface at \(10 \mathrm{~m} / \mathrm{s}\) and then rolls up a smooth \(3^{\circ}\) incline. The maximum height reached by the sphere is \(\left(g=9.8 \mathrm{~m} / \mathrm{s}^{2}\right)\)

1 \(10 \mathrm{~m}\)
2 \(4.9 \mathrm{~m}\)
3 \(14.2 \mathrm{~m}\)
4 \(7.1 \mathrm{~m}\)
Rotational Motion

150462 The acceleration of the centre of mass of a uniform solid disc rolling down an inclined plane of angle \(\alpha\) is

1 \(g \sin \alpha\)
2 \(2 / 3 g \sin \alpha\)
3 \(1 / 2 \mathrm{~g} \sin \alpha\)
4 \(1 / 3 \mathrm{~g} \sin \alpha\)
Rotational Motion

150463 A solid sphere of mass \(1 \mathrm{~kg}\), radius \(10 \mathrm{~cm}\) rolls down an inclined plane of height \(7 \mathrm{~m}\). The velocity of its centre as it reaches the ground level is

1 \(7 \mathrm{~m} / \mathrm{s}\)
2 \(10 \mathrm{~m} / \mathrm{s}\)
3 \(15 \mathrm{~m} / \mathrm{s}\)
4 \(20 \mathrm{~m} / \mathrm{s}\)