A symmetrical block of mass M has a hemispherical notch of radius R. A small particle of mass m slides without friction inside the notch. Find the time period of small oscillation of the particle and block.

Question

G1 Physics · Accepted Answer

For small motion of the particle relative to the moving block, the effective inertial mass is the reduced mass μ=mM/(m+M). With angular displacement θ, the restoring potential is (1/2)mgRθ² and kinetic energy is (1/2)μR²θ̇². Thus ω²=mgR/(μR²)=g(M+m)/(MR), giving T=2π√[R/(g(1+m/M))]. Correct answer: A.