Let I₁ and I₂ be the moments of inertia of two bodies of identical geometrical shape, the first made of aluminum and the second of iron.
A. I₁ < I₂

B. I₁ = I₂

C. I₁ > I₂

D. relation between I₁ and I₂ depends on the actual shapes of the bodies.

Why does a solid sphere have smaller moment of inertia than a hollow cylinder of same mass and radius, about an axis passing through their axes of symmetry?

With reference to Fig. 7.6 of a cube of edge an and mass m, state whether the following are true or false. (O is the centre of the cube.)

Let I₁ and I₂ be the moments of inertia of two bodies of identical geometrical shape, the first made of aluminum and the second of iron.

A circular disc A of radius r is made from an iron plate of thickness t and another circular disc B of radius 4r is made from an iron plate of thickness t/4. The relation between the moments of inertia I_A and I_B is

If the ice at the poles melts and flows towards the equator, how will it affect the duration of day-night?

A closed cylindrical tube containing some water (not filling the entire tube) lies in a horizontal plane. If the tube is rotated about a perpendicular bisector, the moment of inertia of water about the axis

Equal torques act on the discs A and B of the previous problem, initially both being at rest. At a later instant, the linear speeds of a point on the rim of A and another point on the rim of B are and respectively. We have

A body having its center of mass at the origin has three of its particles at (a,0,0) (0, a,0), (0,0, a). The moments of inertia of the body about the X and Y axes are

0.2 kgm² each. The moment of inertia about the Z-axis

The moment of inertia of a uniform semicircular wire of mass M and radius r about a line perpendicular to the plane of the wire through the center is

A. Prove the theorem of perpendicular axes.

(Hint: Square of the distance of a point (x, y) in the x–y plane from an axis through the origin and perpendicular to the plane is x² + y²).

B. Prove the theorem of parallel axes.