01. Angular Displacement, Velocity and Acceleration
Rotational Motion

149788 A rope is wound around a solid cylinder of mass \(1 \mathrm{~kg}\) and radius \(0.4 \mathrm{~m}\). What is the angular acceleration of cylinder, if the rope is pulled with a force of \(25 \mathrm{~N}\) ?
(cylinder is rotating about its own axis)

1 \(125 \mathrm{rad} / \mathrm{s}^{2}\)
2 \(50 \mathrm{rad} / \mathrm{s}^{2}\)
3 \(10 \mathrm{rad} / \mathrm{s}^{2}\)
4 \(1 \mathrm{rad} / \mathrm{s}^{2}\)
Rotational Motion

149789 A disc of radius \(0.4 \mathrm{~m}\) and mass \(1 \mathrm{~kg}\) rotates about an axis passing through its centre and perpendicular to its plane. The angular acceleration is \(10 \mathrm{rad} / \mathrm{s}^{2}\). The tangential force applied to the rim of the disc is

1 \(2 \mathrm{~N}\)
2 \(4 \mathrm{~N}\)
3 \(3 \mathrm{~N}\)
4 \(1 \mathrm{~N}\)
Rotational Motion

149790 A disc rolls down a smooth inclined plane without slipping. An inclined plane make an angle of \(60^{\circ}\) with the vertical. The linear acceleration of the disc along the inclined plane is
\(\left(g=\right.\) acceleration due to gravity, \(\sin 30^{\circ}=\cos\) \(60^{\circ}=\frac{1}{2}, \sin 60^{\circ}=\cos 30^{\circ}=\frac{\sqrt{3}}{2}\) )

1 \(\frac{g}{9}\)
2 \(\frac{g}{6}\)
3 \(\frac{g}{3}\)
4 \(\frac{\mathrm{g}}{18}\)
Rotational Motion

149791 A horizontal circular platform of mass \(100 \mathrm{~kg}\) is rotating at 5 r.p.m. about vertical axis passing through its centre. A child of mass 20 \(\mathrm{kg}\) is standing on the edge of platform. If the child comes to the centre of platform then frequency of rotation will become

1 7 r.p.m.
2 9 r.p.m.
3 5 r.p.m.
4 12 r.p.m.
Rotational Motion

149793 In non uniform circular motion, the ratio of tangential to radial acceleration is \((r=\) radius of circle, \(v=\) speed of the particle, \(\alpha=\) angular acceleration)

1 \(\frac{\alpha^{2} r^{2}}{v}\)
2 \(\frac{\alpha^{2} r}{v^{2}}\)
3 \(\frac{\alpha \mathrm{r}^{2}}{\mathrm{v}^{2}}\)
4 \(\frac{v^{2}}{r^{2} \alpha}\)
Rotational Motion

149788 A rope is wound around a solid cylinder of mass \(1 \mathrm{~kg}\) and radius \(0.4 \mathrm{~m}\). What is the angular acceleration of cylinder, if the rope is pulled with a force of \(25 \mathrm{~N}\) ?
(cylinder is rotating about its own axis)

1 \(125 \mathrm{rad} / \mathrm{s}^{2}\)
2 \(50 \mathrm{rad} / \mathrm{s}^{2}\)
3 \(10 \mathrm{rad} / \mathrm{s}^{2}\)
4 \(1 \mathrm{rad} / \mathrm{s}^{2}\)
Rotational Motion

149789 A disc of radius \(0.4 \mathrm{~m}\) and mass \(1 \mathrm{~kg}\) rotates about an axis passing through its centre and perpendicular to its plane. The angular acceleration is \(10 \mathrm{rad} / \mathrm{s}^{2}\). The tangential force applied to the rim of the disc is

1 \(2 \mathrm{~N}\)
2 \(4 \mathrm{~N}\)
3 \(3 \mathrm{~N}\)
4 \(1 \mathrm{~N}\)
Rotational Motion

149790 A disc rolls down a smooth inclined plane without slipping. An inclined plane make an angle of \(60^{\circ}\) with the vertical. The linear acceleration of the disc along the inclined plane is
\(\left(g=\right.\) acceleration due to gravity, \(\sin 30^{\circ}=\cos\) \(60^{\circ}=\frac{1}{2}, \sin 60^{\circ}=\cos 30^{\circ}=\frac{\sqrt{3}}{2}\) )

1 \(\frac{g}{9}\)
2 \(\frac{g}{6}\)
3 \(\frac{g}{3}\)
4 \(\frac{\mathrm{g}}{18}\)
Rotational Motion

149791 A horizontal circular platform of mass \(100 \mathrm{~kg}\) is rotating at 5 r.p.m. about vertical axis passing through its centre. A child of mass 20 \(\mathrm{kg}\) is standing on the edge of platform. If the child comes to the centre of platform then frequency of rotation will become

1 7 r.p.m.
2 9 r.p.m.
3 5 r.p.m.
4 12 r.p.m.
Rotational Motion

149793 In non uniform circular motion, the ratio of tangential to radial acceleration is \((r=\) radius of circle, \(v=\) speed of the particle, \(\alpha=\) angular acceleration)

1 \(\frac{\alpha^{2} r^{2}}{v}\)
2 \(\frac{\alpha^{2} r}{v^{2}}\)
3 \(\frac{\alpha \mathrm{r}^{2}}{\mathrm{v}^{2}}\)
4 \(\frac{v^{2}}{r^{2} \alpha}\)
Rotational Motion

149788 A rope is wound around a solid cylinder of mass \(1 \mathrm{~kg}\) and radius \(0.4 \mathrm{~m}\). What is the angular acceleration of cylinder, if the rope is pulled with a force of \(25 \mathrm{~N}\) ?
(cylinder is rotating about its own axis)

1 \(125 \mathrm{rad} / \mathrm{s}^{2}\)
2 \(50 \mathrm{rad} / \mathrm{s}^{2}\)
3 \(10 \mathrm{rad} / \mathrm{s}^{2}\)
4 \(1 \mathrm{rad} / \mathrm{s}^{2}\)
Rotational Motion

149789 A disc of radius \(0.4 \mathrm{~m}\) and mass \(1 \mathrm{~kg}\) rotates about an axis passing through its centre and perpendicular to its plane. The angular acceleration is \(10 \mathrm{rad} / \mathrm{s}^{2}\). The tangential force applied to the rim of the disc is

1 \(2 \mathrm{~N}\)
2 \(4 \mathrm{~N}\)
3 \(3 \mathrm{~N}\)
4 \(1 \mathrm{~N}\)
Rotational Motion

149790 A disc rolls down a smooth inclined plane without slipping. An inclined plane make an angle of \(60^{\circ}\) with the vertical. The linear acceleration of the disc along the inclined plane is
\(\left(g=\right.\) acceleration due to gravity, \(\sin 30^{\circ}=\cos\) \(60^{\circ}=\frac{1}{2}, \sin 60^{\circ}=\cos 30^{\circ}=\frac{\sqrt{3}}{2}\) )

1 \(\frac{g}{9}\)
2 \(\frac{g}{6}\)
3 \(\frac{g}{3}\)
4 \(\frac{\mathrm{g}}{18}\)
Rotational Motion

149791 A horizontal circular platform of mass \(100 \mathrm{~kg}\) is rotating at 5 r.p.m. about vertical axis passing through its centre. A child of mass 20 \(\mathrm{kg}\) is standing on the edge of platform. If the child comes to the centre of platform then frequency of rotation will become

1 7 r.p.m.
2 9 r.p.m.
3 5 r.p.m.
4 12 r.p.m.
Rotational Motion

149793 In non uniform circular motion, the ratio of tangential to radial acceleration is \((r=\) radius of circle, \(v=\) speed of the particle, \(\alpha=\) angular acceleration)

1 \(\frac{\alpha^{2} r^{2}}{v}\)
2 \(\frac{\alpha^{2} r}{v^{2}}\)
3 \(\frac{\alpha \mathrm{r}^{2}}{\mathrm{v}^{2}}\)
4 \(\frac{v^{2}}{r^{2} \alpha}\)
Rotational Motion

149788 A rope is wound around a solid cylinder of mass \(1 \mathrm{~kg}\) and radius \(0.4 \mathrm{~m}\). What is the angular acceleration of cylinder, if the rope is pulled with a force of \(25 \mathrm{~N}\) ?
(cylinder is rotating about its own axis)

1 \(125 \mathrm{rad} / \mathrm{s}^{2}\)
2 \(50 \mathrm{rad} / \mathrm{s}^{2}\)
3 \(10 \mathrm{rad} / \mathrm{s}^{2}\)
4 \(1 \mathrm{rad} / \mathrm{s}^{2}\)
Rotational Motion

149789 A disc of radius \(0.4 \mathrm{~m}\) and mass \(1 \mathrm{~kg}\) rotates about an axis passing through its centre and perpendicular to its plane. The angular acceleration is \(10 \mathrm{rad} / \mathrm{s}^{2}\). The tangential force applied to the rim of the disc is

1 \(2 \mathrm{~N}\)
2 \(4 \mathrm{~N}\)
3 \(3 \mathrm{~N}\)
4 \(1 \mathrm{~N}\)
Rotational Motion

149790 A disc rolls down a smooth inclined plane without slipping. An inclined plane make an angle of \(60^{\circ}\) with the vertical. The linear acceleration of the disc along the inclined plane is
\(\left(g=\right.\) acceleration due to gravity, \(\sin 30^{\circ}=\cos\) \(60^{\circ}=\frac{1}{2}, \sin 60^{\circ}=\cos 30^{\circ}=\frac{\sqrt{3}}{2}\) )

1 \(\frac{g}{9}\)
2 \(\frac{g}{6}\)
3 \(\frac{g}{3}\)
4 \(\frac{\mathrm{g}}{18}\)
Rotational Motion

149791 A horizontal circular platform of mass \(100 \mathrm{~kg}\) is rotating at 5 r.p.m. about vertical axis passing through its centre. A child of mass 20 \(\mathrm{kg}\) is standing on the edge of platform. If the child comes to the centre of platform then frequency of rotation will become

1 7 r.p.m.
2 9 r.p.m.
3 5 r.p.m.
4 12 r.p.m.
Rotational Motion

149793 In non uniform circular motion, the ratio of tangential to radial acceleration is \((r=\) radius of circle, \(v=\) speed of the particle, \(\alpha=\) angular acceleration)

1 \(\frac{\alpha^{2} r^{2}}{v}\)
2 \(\frac{\alpha^{2} r}{v^{2}}\)
3 \(\frac{\alpha \mathrm{r}^{2}}{\mathrm{v}^{2}}\)
4 \(\frac{v^{2}}{r^{2} \alpha}\)
Rotational Motion

149788 A rope is wound around a solid cylinder of mass \(1 \mathrm{~kg}\) and radius \(0.4 \mathrm{~m}\). What is the angular acceleration of cylinder, if the rope is pulled with a force of \(25 \mathrm{~N}\) ?
(cylinder is rotating about its own axis)

1 \(125 \mathrm{rad} / \mathrm{s}^{2}\)
2 \(50 \mathrm{rad} / \mathrm{s}^{2}\)
3 \(10 \mathrm{rad} / \mathrm{s}^{2}\)
4 \(1 \mathrm{rad} / \mathrm{s}^{2}\)
Rotational Motion

149789 A disc of radius \(0.4 \mathrm{~m}\) and mass \(1 \mathrm{~kg}\) rotates about an axis passing through its centre and perpendicular to its plane. The angular acceleration is \(10 \mathrm{rad} / \mathrm{s}^{2}\). The tangential force applied to the rim of the disc is

1 \(2 \mathrm{~N}\)
2 \(4 \mathrm{~N}\)
3 \(3 \mathrm{~N}\)
4 \(1 \mathrm{~N}\)
Rotational Motion

149790 A disc rolls down a smooth inclined plane without slipping. An inclined plane make an angle of \(60^{\circ}\) with the vertical. The linear acceleration of the disc along the inclined plane is
\(\left(g=\right.\) acceleration due to gravity, \(\sin 30^{\circ}=\cos\) \(60^{\circ}=\frac{1}{2}, \sin 60^{\circ}=\cos 30^{\circ}=\frac{\sqrt{3}}{2}\) )

1 \(\frac{g}{9}\)
2 \(\frac{g}{6}\)
3 \(\frac{g}{3}\)
4 \(\frac{\mathrm{g}}{18}\)
Rotational Motion

149791 A horizontal circular platform of mass \(100 \mathrm{~kg}\) is rotating at 5 r.p.m. about vertical axis passing through its centre. A child of mass 20 \(\mathrm{kg}\) is standing on the edge of platform. If the child comes to the centre of platform then frequency of rotation will become

1 7 r.p.m.
2 9 r.p.m.
3 5 r.p.m.
4 12 r.p.m.
Rotational Motion

149793 In non uniform circular motion, the ratio of tangential to radial acceleration is \((r=\) radius of circle, \(v=\) speed of the particle, \(\alpha=\) angular acceleration)

1 \(\frac{\alpha^{2} r^{2}}{v}\)
2 \(\frac{\alpha^{2} r}{v^{2}}\)
3 \(\frac{\alpha \mathrm{r}^{2}}{\mathrm{v}^{2}}\)
4 \(\frac{v^{2}}{r^{2} \alpha}\)