A light rod of length `l` has two masses `m_1` and `m_2` attached to its two ends. The moment of inertia of the system about an axis perpendicular to the rod and passing through the centre of mass is.

Options

A. `(m _(1) + m _(2) ) l ^(2)`
B. `sqrt ( m _(1) m ^(2)) l ^(2)`
C. `(m _(1) m _(2))/( m _(1) + m _(2)) l ^(2)`
D. `(m _(1) + m _(2))/( m _(1) m _(2)) l ^(2)`

Explanation

`r _(1) = ( m _(2) l )/( m _(1) + m _(2)) , r _(2) = ( m_(1) l )/( m _(1) + m _(2))`
`I _(cm) = m _(1) r _(1) ^(2) + m _(2) r _(2) ^(2) = ( m _(1) m _(2))/( m_(1) + m _(2)) l ^(2)`