The moment of inertia of a thin uniform rod of mass M and length L about an axis perpendicular to the rod, through its centre is I. The moment of inertia of the rod about axis perpendicular to the rod through its end point is

Options

A. `(I)/(4)`
B. `(I)/(2)`
C. 2I
D. 4I

Answer

(d)

Explanation

Moment of inertia of a thin uniform rod about an axis passing through its centre is,
`(I_(XY))=(mL^(2))/(12)`
Moment of inertia about an axis PQ,
`I_(PQ)=I_(XY)+M((L)/(2))^(2)`=`(ML^(2))/(12)+(ML^(2))/(4)`
=`(4ML^(2))/(12)=4((ML^(2))/(12))`
`=4I`.