Question

A thin wire of length 'L' and uniform linear mass density 'm' is bent into a circular loop. The moment of inertia of this loop about the tangential axis and in the plane of the coil is ______.

Options

• `(3"mL"^3)/(4pi^2)`

• `(3"mL"^3)/(8pi^2)`

• `(3"mL"^3)/(16pi^2)`

• `(3"mL"^3)/(2pi^2)`

Answer 1

A thin wire of length 'L' and uniform linear mass density 'm' is bent into a circular loop. The moment of inertia of this loop about the tangential axis and in the plane of the coil is `underline((3"mL"^3)/(8pi^2))`.

Explanation:

The mass of the wire = M = mL

The radius of the circular loop = r `="L"/(2pi)`

The moment of inertia of this loop about the tangential axis in the plane of the coil is

`"I"=3/2"mr"^2=3/2xx"mL"xx"L"^2/(4pi^2)`

`=(3"mL"^3)/(8pi^2)`