Question

A body is rotating about its own axis. Its rotational kinetic energy is x and its angular momentum is y, hence its moment of inertia about the axis is ______.

Options

• `y^2/(2x)`

• `x/(2y)`

• `y/(2x)`

• `x^2/(2y)`

Answer 1

A body is rotating about its own axis. Its rotational kinetic energy is x and its angular momentum is y, hence its moment of inertia about the axis is `underlinebb(y^2/(2x))`.

Explanation:

Rotational kinetic energy, x = `1/2lomega^2` ...........(i)

Angular momentum, y = lω

⇒ ω = `y/l` ..............(ii)

From Eqs. (i) and (ii), we get

`x = 1/2l(y/l)^2`

⇒ l = `y^2/(2x)`