A solid aluminimum sphere of radius `R` has moment of inertia `I` about an axis through its centre. The moment of inertia about a central axis of a solid aluminimum sphere of radius `2 R` is.

Options

A. `1 : 8`
B. `2 : 5`
C. `2 : 3`
D. `1 : 4`

Answer

D

Explanation

Moment of inertia of a solid sphere about its diameter is `l=2/5MR^(2)` …(i)
As the radius of a solid sphere is doubled then the new moment of inertia of the sphere will be
`l'=2/5M(2R)^(2)=8/5MR^(2)` ….(ii)
From Eqs. (i) and (ii), we get
`I/(I')=(2/5MR^(2))/(8/5MR^(2))=1/4=1 : 4`
The ratio of their moment of inertia about any of its diameter is 1 : 4.