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. `m l^(2)`
B. zero
C. `m l^(2)// pi^(2)`
D. `m l^(2)//2 pi^(2)`

Answer

D

Explanation

`pi R = l therefore = (l)/(pi)`
M..I. of ring about its diameter `=(1)/(2)MR^(2)`
`therefore` MI of semicircle `=(1)/(2)m((l)/(pi))^(2)=(ml^(2))/(2pi^(2))`