03. Moment of Inertia, Radius of Gyration
« Previous Topic: 02. Torque, Angular Momentum Next Topic: 04. Equilibrium of Rigid Body »
Rotational Motion

150164 A wheel having moment of inertia \(2 \mathrm{~kg}-\mathrm{m}^{2}\) about its axis, rotates at \(50 \mathrm{rpm}\) about the same axis. The torque required to stop the wheel in one minute is

1 \(\frac{\pi}{10} \mathrm{Nm}\)
2 \(\frac{\pi}{18} \mathrm{Nm}\)
3 \(-\frac{\pi}{12} \mathrm{Nm}\)
4 \(\frac{3 \pi}{8} \mathrm{Nm}\)
AP EAMCET (21.04.2019) Shift-II
Rotational Motion

150165 A solid sphere of \(100 \mathrm{~kg}\) and radius \(10 \mathrm{~m}\) moving in a space becomes a circular disc of radius \(20 \mathrm{~m}\) in one hour. Then the rate of change of moment of inertia in the process is

1 \(\frac{40}{9} \mathrm{kgm}^{2} \mathrm{~s}^{-1}\)
2 \(\frac{10}{9} \mathrm{kgm}^{2} \mathrm{~s}^{-1}\)
3 \(\frac{50}{9} \mathrm{kgm}^{2} \mathrm{~s}^{-1}\)
4 \(\frac{25}{9} \mathrm{kgm}^{2} \mathrm{~s}^{-1}\)
AP EAMCET (20.04.2019) Shift-1
Rotational Motion

150166 From a circular card board of uniform thickness and mass \(M\), a square disc of maximum possible area is cut. If the moment of inertia of the square with the axis of rotation at the centre and perpendicular to the plane of the disc is \(\frac{\mathrm{Ma}^{2}}{6}\),the radius of the circular card board is

1 \(\sqrt{2} \mathrm{a}\)
2 \(\frac{\mathrm{a}}{\sqrt{2}}\)
3 \(2 \mathrm{a}\)
4 \(\frac{1}{2 \mathrm{a}}\)
5 \(2 \sqrt{2} \mathrm{a}\)
Kerala CEE -2018
Rotational Motion

150168 A square frame \(\mathrm{ABCD}\) is formed by four identical rods each of mass ' \(m\) ' and length ' \(l\) '. This frame is in \(X-Y\) plane such that side \(A B\) coincides with \(\mathrm{X}\)-axis and side AD along \(\mathrm{Y}\)-axis. The moment of inertia of the frame about \(X\) axis is

1 \(\frac{5 \mathrm{~m} l^{2}}{3}\)
2 \(\frac{2 \mathrm{~m} l^{2}}{3}\)
3 \(\frac{4 \mathrm{~m} l^{2}}{3}\)
4 \(\frac{\mathrm{m} l^{2}}{12}\)
MHT-CET 2018
Rotational Motion

150169 Find ratio of radius of gyration of a disc and ring of same radii at their tangential axis in plane.

1 \(\sqrt{\frac{5}{6}}\)
2 \(\sqrt{\frac{5}{3}}\)
3 1
4 \(\frac{2}{3}\)
JIPMER-2018
Join With Us for More Updates
Rotational Motion

150164 A wheel having moment of inertia \(2 \mathrm{~kg}-\mathrm{m}^{2}\) about its axis, rotates at \(50 \mathrm{rpm}\) about the same axis. The torque required to stop the wheel in one minute is

1 \(\frac{\pi}{10} \mathrm{Nm}\)
2 \(\frac{\pi}{18} \mathrm{Nm}\)
3 \(-\frac{\pi}{12} \mathrm{Nm}\)
4 \(\frac{3 \pi}{8} \mathrm{Nm}\)
AP EAMCET (21.04.2019) Shift-II
Rotational Motion

150165 A solid sphere of \(100 \mathrm{~kg}\) and radius \(10 \mathrm{~m}\) moving in a space becomes a circular disc of radius \(20 \mathrm{~m}\) in one hour. Then the rate of change of moment of inertia in the process is

1 \(\frac{40}{9} \mathrm{kgm}^{2} \mathrm{~s}^{-1}\)
2 \(\frac{10}{9} \mathrm{kgm}^{2} \mathrm{~s}^{-1}\)
3 \(\frac{50}{9} \mathrm{kgm}^{2} \mathrm{~s}^{-1}\)
4 \(\frac{25}{9} \mathrm{kgm}^{2} \mathrm{~s}^{-1}\)
AP EAMCET (20.04.2019) Shift-1
Rotational Motion

150166 From a circular card board of uniform thickness and mass \(M\), a square disc of maximum possible area is cut. If the moment of inertia of the square with the axis of rotation at the centre and perpendicular to the plane of the disc is \(\frac{\mathrm{Ma}^{2}}{6}\),the radius of the circular card board is

1 \(\sqrt{2} \mathrm{a}\)
2 \(\frac{\mathrm{a}}{\sqrt{2}}\)
3 \(2 \mathrm{a}\)
4 \(\frac{1}{2 \mathrm{a}}\)
5 \(2 \sqrt{2} \mathrm{a}\)
Kerala CEE -2018
Rotational Motion

150168 A square frame \(\mathrm{ABCD}\) is formed by four identical rods each of mass ' \(m\) ' and length ' \(l\) '. This frame is in \(X-Y\) plane such that side \(A B\) coincides with \(\mathrm{X}\)-axis and side AD along \(\mathrm{Y}\)-axis. The moment of inertia of the frame about \(X\) axis is

1 \(\frac{5 \mathrm{~m} l^{2}}{3}\)
2 \(\frac{2 \mathrm{~m} l^{2}}{3}\)
3 \(\frac{4 \mathrm{~m} l^{2}}{3}\)
4 \(\frac{\mathrm{m} l^{2}}{12}\)
MHT-CET 2018
Rotational Motion

150169 Find ratio of radius of gyration of a disc and ring of same radii at their tangential axis in plane.

1 \(\sqrt{\frac{5}{6}}\)
2 \(\sqrt{\frac{5}{3}}\)
3 1
4 \(\frac{2}{3}\)
JIPMER-2018
For More Updates join with Us
Rotational Motion

150164 A wheel having moment of inertia \(2 \mathrm{~kg}-\mathrm{m}^{2}\) about its axis, rotates at \(50 \mathrm{rpm}\) about the same axis. The torque required to stop the wheel in one minute is

1 \(\frac{\pi}{10} \mathrm{Nm}\)
2 \(\frac{\pi}{18} \mathrm{Nm}\)
3 \(-\frac{\pi}{12} \mathrm{Nm}\)
4 \(\frac{3 \pi}{8} \mathrm{Nm}\)
AP EAMCET (21.04.2019) Shift-II
Rotational Motion

150165 A solid sphere of \(100 \mathrm{~kg}\) and radius \(10 \mathrm{~m}\) moving in a space becomes a circular disc of radius \(20 \mathrm{~m}\) in one hour. Then the rate of change of moment of inertia in the process is

1 \(\frac{40}{9} \mathrm{kgm}^{2} \mathrm{~s}^{-1}\)
2 \(\frac{10}{9} \mathrm{kgm}^{2} \mathrm{~s}^{-1}\)
3 \(\frac{50}{9} \mathrm{kgm}^{2} \mathrm{~s}^{-1}\)
4 \(\frac{25}{9} \mathrm{kgm}^{2} \mathrm{~s}^{-1}\)
AP EAMCET (20.04.2019) Shift-1
Rotational Motion

150166 From a circular card board of uniform thickness and mass \(M\), a square disc of maximum possible area is cut. If the moment of inertia of the square with the axis of rotation at the centre and perpendicular to the plane of the disc is \(\frac{\mathrm{Ma}^{2}}{6}\),the radius of the circular card board is

1 \(\sqrt{2} \mathrm{a}\)
2 \(\frac{\mathrm{a}}{\sqrt{2}}\)
3 \(2 \mathrm{a}\)
4 \(\frac{1}{2 \mathrm{a}}\)
5 \(2 \sqrt{2} \mathrm{a}\)
Kerala CEE -2018
Rotational Motion

150168 A square frame \(\mathrm{ABCD}\) is formed by four identical rods each of mass ' \(m\) ' and length ' \(l\) '. This frame is in \(X-Y\) plane such that side \(A B\) coincides with \(\mathrm{X}\)-axis and side AD along \(\mathrm{Y}\)-axis. The moment of inertia of the frame about \(X\) axis is

1 \(\frac{5 \mathrm{~m} l^{2}}{3}\)
2 \(\frac{2 \mathrm{~m} l^{2}}{3}\)
3 \(\frac{4 \mathrm{~m} l^{2}}{3}\)
4 \(\frac{\mathrm{m} l^{2}}{12}\)
MHT-CET 2018
Rotational Motion

150169 Find ratio of radius of gyration of a disc and ring of same radii at their tangential axis in plane.

1 \(\sqrt{\frac{5}{6}}\)
2 \(\sqrt{\frac{5}{3}}\)
3 1
4 \(\frac{2}{3}\)
JIPMER-2018
NEET DIGITAL LIBRARY
Rotational Motion

150164 A wheel having moment of inertia \(2 \mathrm{~kg}-\mathrm{m}^{2}\) about its axis, rotates at \(50 \mathrm{rpm}\) about the same axis. The torque required to stop the wheel in one minute is

1 \(\frac{\pi}{10} \mathrm{Nm}\)
2 \(\frac{\pi}{18} \mathrm{Nm}\)
3 \(-\frac{\pi}{12} \mathrm{Nm}\)
4 \(\frac{3 \pi}{8} \mathrm{Nm}\)
AP EAMCET (21.04.2019) Shift-II
Rotational Motion

150165 A solid sphere of \(100 \mathrm{~kg}\) and radius \(10 \mathrm{~m}\) moving in a space becomes a circular disc of radius \(20 \mathrm{~m}\) in one hour. Then the rate of change of moment of inertia in the process is

1 \(\frac{40}{9} \mathrm{kgm}^{2} \mathrm{~s}^{-1}\)
2 \(\frac{10}{9} \mathrm{kgm}^{2} \mathrm{~s}^{-1}\)
3 \(\frac{50}{9} \mathrm{kgm}^{2} \mathrm{~s}^{-1}\)
4 \(\frac{25}{9} \mathrm{kgm}^{2} \mathrm{~s}^{-1}\)
AP EAMCET (20.04.2019) Shift-1
Rotational Motion

150166 From a circular card board of uniform thickness and mass \(M\), a square disc of maximum possible area is cut. If the moment of inertia of the square with the axis of rotation at the centre and perpendicular to the plane of the disc is \(\frac{\mathrm{Ma}^{2}}{6}\),the radius of the circular card board is

1 \(\sqrt{2} \mathrm{a}\)
2 \(\frac{\mathrm{a}}{\sqrt{2}}\)
3 \(2 \mathrm{a}\)
4 \(\frac{1}{2 \mathrm{a}}\)
5 \(2 \sqrt{2} \mathrm{a}\)
Kerala CEE -2018
Rotational Motion

150168 A square frame \(\mathrm{ABCD}\) is formed by four identical rods each of mass ' \(m\) ' and length ' \(l\) '. This frame is in \(X-Y\) plane such that side \(A B\) coincides with \(\mathrm{X}\)-axis and side AD along \(\mathrm{Y}\)-axis. The moment of inertia of the frame about \(X\) axis is

1 \(\frac{5 \mathrm{~m} l^{2}}{3}\)
2 \(\frac{2 \mathrm{~m} l^{2}}{3}\)
3 \(\frac{4 \mathrm{~m} l^{2}}{3}\)
4 \(\frac{\mathrm{m} l^{2}}{12}\)
MHT-CET 2018
Rotational Motion

150169 Find ratio of radius of gyration of a disc and ring of same radii at their tangential axis in plane.

1 \(\sqrt{\frac{5}{6}}\)
2 \(\sqrt{\frac{5}{3}}\)
3 1
4 \(\frac{2}{3}\)
JIPMER-2018
Join With Us for More Updates
Rotational Motion

150164 A wheel having moment of inertia \(2 \mathrm{~kg}-\mathrm{m}^{2}\) about its axis, rotates at \(50 \mathrm{rpm}\) about the same axis. The torque required to stop the wheel in one minute is

1 \(\frac{\pi}{10} \mathrm{Nm}\)
2 \(\frac{\pi}{18} \mathrm{Nm}\)
3 \(-\frac{\pi}{12} \mathrm{Nm}\)
4 \(\frac{3 \pi}{8} \mathrm{Nm}\)
AP EAMCET (21.04.2019) Shift-II
Rotational Motion

150165 A solid sphere of \(100 \mathrm{~kg}\) and radius \(10 \mathrm{~m}\) moving in a space becomes a circular disc of radius \(20 \mathrm{~m}\) in one hour. Then the rate of change of moment of inertia in the process is

1 \(\frac{40}{9} \mathrm{kgm}^{2} \mathrm{~s}^{-1}\)
2 \(\frac{10}{9} \mathrm{kgm}^{2} \mathrm{~s}^{-1}\)
3 \(\frac{50}{9} \mathrm{kgm}^{2} \mathrm{~s}^{-1}\)
4 \(\frac{25}{9} \mathrm{kgm}^{2} \mathrm{~s}^{-1}\)
AP EAMCET (20.04.2019) Shift-1
Rotational Motion

150166 From a circular card board of uniform thickness and mass \(M\), a square disc of maximum possible area is cut. If the moment of inertia of the square with the axis of rotation at the centre and perpendicular to the plane of the disc is \(\frac{\mathrm{Ma}^{2}}{6}\),the radius of the circular card board is

1 \(\sqrt{2} \mathrm{a}\)
2 \(\frac{\mathrm{a}}{\sqrt{2}}\)
3 \(2 \mathrm{a}\)
4 \(\frac{1}{2 \mathrm{a}}\)
5 \(2 \sqrt{2} \mathrm{a}\)
Kerala CEE -2018
Rotational Motion

150168 A square frame \(\mathrm{ABCD}\) is formed by four identical rods each of mass ' \(m\) ' and length ' \(l\) '. This frame is in \(X-Y\) plane such that side \(A B\) coincides with \(\mathrm{X}\)-axis and side AD along \(\mathrm{Y}\)-axis. The moment of inertia of the frame about \(X\) axis is

1 \(\frac{5 \mathrm{~m} l^{2}}{3}\)
2 \(\frac{2 \mathrm{~m} l^{2}}{3}\)
3 \(\frac{4 \mathrm{~m} l^{2}}{3}\)
4 \(\frac{\mathrm{m} l^{2}}{12}\)
MHT-CET 2018
Rotational Motion

150169 Find ratio of radius of gyration of a disc and ring of same radii at their tangential axis in plane.

1 \(\sqrt{\frac{5}{6}}\)
2 \(\sqrt{\frac{5}{3}}\)
3 1
4 \(\frac{2}{3}\)
JIPMER-2018