Masses m and m/2 are connected to the ends of a massless rigid rod of length l. The rod is suspended by a torsion wire of constant k at the centre of mass. If rotated by θ₀ and released, the tension in the rod when it passes through mean position is:

Question

G1 Physics · Accepted Answer

Masses m and m/2 are separated by l. Their distances from the centre of mass are l/3 and 2l/3. Moment of inertia I=m(l/3)²+(m/2)(2l/3)²=ml²/3. At the mean position, torsional energy gives (1/2)IΩ²=(1/2)kθ₀², so Ω²=3kθ₀²/(ml²). The lighter mass needs centripetal force (m/2)Ω²(2l/3)=kθ₀²/l, which is the rod tension. Correct option: 4.