In the shown figure inside a fixed hollow cylinder with vertical axis a pendulum is rotating in a conical path with its axis same as that of the cylinder with uniform angular velocity. Radius of cylinder is 30 cm, length of string is 50 cm and mass of bob is 400 gm. The bob makes contact with the inner frictionless wall of the cylinder while moving :-

Question

G1 Physics · Accepted Answer

Geometry gives sinθ=0.3/0.5=0.6 and cosθ=0.8. Vertical balance gives T cosθ=mg, so T=5 N. Radially, T sinθ+N=mω²r; contact requires N≥0, giving ω(min)=5 rad/s. At ω=10 rad/s, N=0.4(10²)(0.3)-3=9 N. Hence A,B,C.