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))`
D. `(m_(1)+m_(2))/(m_(1)m_(2)) l^(2)`

Answer

C

Explanation

`I_(cm) = m_(1)r_(1)^(2) +m_(2)r_(2)^(2)=(m_(1)m_(2))/(m_(1)+m_(2))l^(2)`