03. Moment of Inertia, Radius of Gyration
Rotational Motion

150156 A thin ring having mass \(100 \mathrm{~g}\) and radius \(10 \mathrm{~cm}\) is rotating about its axis with frequency \(1 \mathrm{~Hz}\). Four objects each of mass \(12.5 \mathrm{~g}\) are kept gently to the opposite ends of two perpendicular diameters of the ring. The new frequency of rotation of the ring will be

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

150157 Four metal rods each of mass ' \(M\) ' and length ' \(L\) ' are welded to form of a square as shown. What is M.I. of the system about axis 'AB'?

axis of rotation

1 \(\frac{2}{3} \mathrm{ML}^{2}\)
2 \(\frac{\mathrm{ML}^{2}}{6}\)
3 \(\frac{\mathrm{ML}^{2}}{3}\)
4 \(\frac{\mathrm{ML}^{2}}{2}\)
Rotational Motion

150158 Three identical rods each of mass ' \(M\) ' and length ' \(L\) ' are joined to form a symbol ' \(H\) '. The moment of inertia of the system about one of the sides of ' \(H\) ' is

1 \(\mathrm{ML}^{2} / 6\)
2 \(4 \mathrm{ML}^{2} / 3\)
3 \(2 \mathrm{ML}^{2} / 3\)
4 \(\mathrm{ML}^{2} / 2\)
Rotational Motion

150159 If radius of the solid sphere is doubled by keeping its mass constant, the ratio of their moment of inertia about any of its diameter is

1 \(1: 4\)
2 \(2: 3\)
3 \(2: 5\)
4 \(1: 8\)
Rotational Motion

150156 A thin ring having mass \(100 \mathrm{~g}\) and radius \(10 \mathrm{~cm}\) is rotating about its axis with frequency \(1 \mathrm{~Hz}\). Four objects each of mass \(12.5 \mathrm{~g}\) are kept gently to the opposite ends of two perpendicular diameters of the ring. The new frequency of rotation of the ring will be

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

150157 Four metal rods each of mass ' \(M\) ' and length ' \(L\) ' are welded to form of a square as shown. What is M.I. of the system about axis 'AB'?

axis of rotation

1 \(\frac{2}{3} \mathrm{ML}^{2}\)
2 \(\frac{\mathrm{ML}^{2}}{6}\)
3 \(\frac{\mathrm{ML}^{2}}{3}\)
4 \(\frac{\mathrm{ML}^{2}}{2}\)
Rotational Motion

150158 Three identical rods each of mass ' \(M\) ' and length ' \(L\) ' are joined to form a symbol ' \(H\) '. The moment of inertia of the system about one of the sides of ' \(H\) ' is

1 \(\mathrm{ML}^{2} / 6\)
2 \(4 \mathrm{ML}^{2} / 3\)
3 \(2 \mathrm{ML}^{2} / 3\)
4 \(\mathrm{ML}^{2} / 2\)
Rotational Motion

150159 If radius of the solid sphere is doubled by keeping its mass constant, the ratio of their moment of inertia about any of its diameter is

1 \(1: 4\)
2 \(2: 3\)
3 \(2: 5\)
4 \(1: 8\)
Rotational Motion

150156 A thin ring having mass \(100 \mathrm{~g}\) and radius \(10 \mathrm{~cm}\) is rotating about its axis with frequency \(1 \mathrm{~Hz}\). Four objects each of mass \(12.5 \mathrm{~g}\) are kept gently to the opposite ends of two perpendicular diameters of the ring. The new frequency of rotation of the ring will be

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

150157 Four metal rods each of mass ' \(M\) ' and length ' \(L\) ' are welded to form of a square as shown. What is M.I. of the system about axis 'AB'?

axis of rotation

1 \(\frac{2}{3} \mathrm{ML}^{2}\)
2 \(\frac{\mathrm{ML}^{2}}{6}\)
3 \(\frac{\mathrm{ML}^{2}}{3}\)
4 \(\frac{\mathrm{ML}^{2}}{2}\)
Rotational Motion

150158 Three identical rods each of mass ' \(M\) ' and length ' \(L\) ' are joined to form a symbol ' \(H\) '. The moment of inertia of the system about one of the sides of ' \(H\) ' is

1 \(\mathrm{ML}^{2} / 6\)
2 \(4 \mathrm{ML}^{2} / 3\)
3 \(2 \mathrm{ML}^{2} / 3\)
4 \(\mathrm{ML}^{2} / 2\)
Rotational Motion

150159 If radius of the solid sphere is doubled by keeping its mass constant, the ratio of their moment of inertia about any of its diameter is

1 \(1: 4\)
2 \(2: 3\)
3 \(2: 5\)
4 \(1: 8\)
Rotational Motion

150156 A thin ring having mass \(100 \mathrm{~g}\) and radius \(10 \mathrm{~cm}\) is rotating about its axis with frequency \(1 \mathrm{~Hz}\). Four objects each of mass \(12.5 \mathrm{~g}\) are kept gently to the opposite ends of two perpendicular diameters of the ring. The new frequency of rotation of the ring will be

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

150157 Four metal rods each of mass ' \(M\) ' and length ' \(L\) ' are welded to form of a square as shown. What is M.I. of the system about axis 'AB'?

axis of rotation

1 \(\frac{2}{3} \mathrm{ML}^{2}\)
2 \(\frac{\mathrm{ML}^{2}}{6}\)
3 \(\frac{\mathrm{ML}^{2}}{3}\)
4 \(\frac{\mathrm{ML}^{2}}{2}\)
Rotational Motion

150158 Three identical rods each of mass ' \(M\) ' and length ' \(L\) ' are joined to form a symbol ' \(H\) '. The moment of inertia of the system about one of the sides of ' \(H\) ' is

1 \(\mathrm{ML}^{2} / 6\)
2 \(4 \mathrm{ML}^{2} / 3\)
3 \(2 \mathrm{ML}^{2} / 3\)
4 \(\mathrm{ML}^{2} / 2\)
Rotational Motion

150159 If radius of the solid sphere is doubled by keeping its mass constant, the ratio of their moment of inertia about any of its diameter is

1 \(1: 4\)
2 \(2: 3\)
3 \(2: 5\)
4 \(1: 8\)