Question

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 ______.

Options

• 1 : 8

• 2 : 5

• 2 : 3

• 1 : 4

Answer 1

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 : 4.

Explanation:

Moment of inertia of a solid sphere about its diameter is I = `2/5 "MR"^2`    ...(i)

As the radius of a solid sphere is doubled then the new moment of inertia of the sphere will be

I' = `2/5 "M"(2"R")^2 = 8/5 "MR"^2`    ...(ii)

From Eqs. (i) and (ii), we get

`"I"/"I'" = (2/5 "MR"^2)/(8/5 "MR"^2) = 1/4` = 1 : 4

The ratio of their moment of Inertia about any of its diameter is 1 : 4