A uniform rod of mass m and length / makes a constant angle `theta` with an axis of rotation which passes through one end of the rod. Its moment of inertia about this axis is

Options

A. `(ml^(2))/(3)`
B. `(ml^(2))/(3) sin theta`
C. `(ml^(2))/(3) sin^(2) theta`
D. `(ml^2)/(3) cos^(2) theta`

Answer

C

Explanation

Mass of an arbitrary element dx = `((m)/(l))` dx
Moment of inertia of the element about the axis = `((m)/(l) ""dx) (x sin theta)^(2)`
`I = (m)/(l) sin^(2) theta int_(0)^(1) x^(2) dx = (ml^(2))/(3) sin^(2) theta`