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

A light rod of length l has two masses m_(1) and m_(2) attached to its

1.	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
Answer» `(m_1 m_2 )/(m_(1) + m_(2)) "" L^(2)` `(m_1 + m_2)/(m_1 m_2) ""l^(2)` `(m_(1) + m_(2)) l^2` `sqrt(m_(1) m_(2)) l^(2)` Solution :Here , `l_(1) + l_(2) = l` Centre of mass of the system , `I_(1) = (m_(1) xx 0 + m_(2) xx l)/(m_(1) + m_(2)) = (m_(2) l)/(m_(1) + m_(2))` `l_(2) = l - l_(1) = (m_(1) l)/(m_(1) + m_(2))` REQUIRED moment of inertia of the system , `I = m_(1) l_(1)^(2) + m_(2) l_(2)^(2) = (m_(1) m_(2)^(2) + m_(2)m_(1)^(2)) (l^(2))/((m_(1) + m_(2))^(2))` `= (m_(1) m_(2) (m_(1) + m_(2))l^(2))/((m_(1) + m_(2))^(2)) = (m_(1) m_(2))/(m_(1) + m_(2))""l^(2)`