One solid sphere `A` and another hollow sphere `B` are of same mass and same outer radii. Their moment of inertia about their diameters are respectively `I_(A)` and `I_(B)` such that.

Options

A. `I_(A) = I_(B)`
B. `I_(A) gt I_(B)`
C. `I_(A) lt I_(B)`
D. `I_(A)//I_(B) = d_(A)//d_(B)`

Answer

C

Explanation

Let same mass and same outer radii of solid sphere and hollow sphere are `M` and `R` respectively.
The moment the moment of inertia of hollow sphere (spherical shell) `B` about its diameter
`I_(A) = (2)/(5) MR^(2)` …(1)
Similarly the moment of inertia of hollow sphere (spherical shell) `B` about its diameter.
`I_(B) = (2)/(5) MR^(2)` ...(ii)
It is clear from eqs. (i) and (ii), `I_(A) lt I_(B)`.