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)` respectivley. 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

(d) 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) = I_(PQ) + I_(RS) = (m l^2)/(12)`
by perpendicular axis theorem.