Question

Consider a uniform semicircular wire of mass M and radius R as shown in the figure. Its M.I. about an axis ZZ' is ____________.

Options

• MR²

• `"MR"^2/2`

• `(2"MR"^2)/3`

• `"MR"^2/4`

Answer 1

Consider a uniform semicircular wire of mass M and radius R as shown in the figure. Its M.I. about an axis ZZ' is `"MR"^2/2`.

Explanation:

Consider complete ring of mass 2M,

`"I"_"cm" = 2"MR"^2 ("using" bot^"r" "axes theorem")`

`therefore "I"_"z" = 1/2 (2"MR"^2) = "MR"^2`

But given ring is in semicircle with mass M,

`"I" = 1/2 xx "I"_"z" = "MR"^2/2`