A thin wire of length l and mass m is bent in the form of a semicircle as shown in the figure. Its moment of inertia about an axis joining its free ends will be

Options

A. `ml^(2)`
B. zero
C. `ml^(2)//2pi^(2)`
D. `ml^(2)//2pi^(2)`

Answer

C

Explanation

Given that, length of wire
= Perimeter of semicircle
or, `" "pir=l`
`:." "r=(1)/(pi)`
Moment of inertia of a right about its diameter `=(1)/(2)mr^(2)`
`:.` Moment of inertia of semicircle
`=(1)/(2)[m((1)/(pi))^(2)]=(ml^(2))/(2pi^(2))`