The moment of inertia of a uniform thin rod of mass m and length L about two axis PQ and RS passing through centre of rod C and in the plane of the rod are `I_(PQ)` and `I_(RS)` respectively. Then `I_(PQ) +I_(RS)` is equal to

Options

A. `(m l^(2))/(3)`
B. `(ml^(2))/(2)`
C. `(ml^(2))/(4)`
D. `(ml^(2))/(12)`

Answer

D

Explanation

The MI of rod about axis PQ figure (a) and MI of rod about axis P'Q' figure (b) are same by symmetry

`:. I_(PQ)+I_(RS)=O_(PQ)+I_(RS)=(ml^(2))/(12)`
by perpendicular axis theorem.