Question

The moment of inertia of a spherical shell and a hemispherical shell of same mass and radius about a tangential axis, passing through $P$ will be

• A. Different
• B. same
• C. data insufficient
• D. none of these

Answer 1

The correct option is B same

The two bodies have same mass and same distribution of mass about the axis along with same dimension.

Therefore they have same moment of Inertia.

Let momentum of inertia of Hemisphere be $M{K}^2$ whose $k$ is radius of gyration

Moment of inertia of hemisphere with same dimention and half the mass $=\frac{M}{2}{K}^2$.

$I$ (two hemisphere) $=\frac{M}{2}{K}^2+\frac{M}{2}{K}^2=M{K}^2$

We ioin the two hemisphere to make a sphere.

$\Rightarrow$ Momentum Inertia of sphere Hemisphere of same mass.