With reference to the figure of a cube of edge \(a\) and mass \(m,\) the following statements are given. (\(O\) is the centre of the cube).
(a) | \(z\)-axis is \(I_z=I_x+I_y\) | The moment of inertia of the cube about the
(b) | \(z'\)-axis is \({I_z}'=I_z+\frac{{ma}^2}{2}\) | The moment of inertia of the cube about the
(c) | \(z''\)-axis is = \(=I_z+\frac{{ma}^2}{2}\) | The moment of inertia of the cube about
(d) | \(I_x=I_y\) |
1. | (a, c) | 2. | (a, d) |
3. | (b, d) | 4. | (b, c) |
Assertion (A): | If the same mass is drawn into the making of a solid sphere and a hollow sphere, the moment of inertia about the diameter of a hollow body is greater than that of a solid body. |
Reason (R): | The moment of inertia depends on the mass distribution from the axis of rotation and in a hollow sphere, more of the mass is further away from the axis of rotation. |
1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
3. | (A) is True but (R) is False. |
4. | Both (A) and (R) are False. |
Assertion (A): | When a body rotates in a circle around any axis, all its particles move along a circle in different radii but with the same angular velocity. |
Reason (R): | The moment of inertia is a vector quantity. |
1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
3. | (A) is True but (R) is False. |
4. | Both (A) and (R) are False. |