In the figure, identical springs are connected to a rod at its upper end and at its midpoint. The rod of mass m and length L is hinged at its lower end. Rotational SHM occurs only if:

Question

G1 Physics · Accepted Answer

For small rotation θ, the upper spring gives torque kL²θ and the midpoint spring gives k(L/2)²θ, total spring torque=(5/4)kL²θ. Gravity gives a destabilizing torque mg(L/2)θ. For stable SHM, (5/4)kL²>mgL/2, so k>2mg/(5L). Correct answer: C.