Question

Two masses m₁ and m₂ are placed at the ends of a weightless rod of length r. Find the moment of inertia of this system about the axis passing through the centre of mass and perpendicular to length of the rod.

Answer 1

Suppose the distance of masses m₁ and m₂ from centre of mass are r₁ and r₂. Therefore from the definition of centre of mass,

Substituting this value of x₁ in equation (1)

\(r_2 = r_1 -\frac{m_2r}{(m_1 + m_2)} = \frac{m_1r + m_2r}{m_1 + m_2} - m_2r\) 

or \(r_2 = \frac{m_1r}{m_1 + m_2}\)

∴ Moment of inertia about axis passing through CM. at right angles to the length of the rod