A horizontal turn table is initially at rest. It starts to rotate in horizontal plane with constant angular acceleration 3 rad/s². A block of mass 1 kg is placed 1 metre away from the axis of rotation on the turn table. A horizontal force F = 5t N where t is in seconds, is acting on the block always towards the center of rotation. The block begins to slip at t = 1s. The coefficient of friction between block and turn table is
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Question

A horizontal turn table is initially at rest. It starts to rotate in horizontal plane with constant angular acceleration 3 rad/s². A block of mass 1 kg is placed 1 metre away from the axis of rotation on the turn table. A horizontal force F = 5t N where t is in seconds, is acting on the block always towards the center of rotation. The block begins to slip at t = 1s. The coefficient of friction between block and turn table is

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G1 Physics · Accepted Answer

At t=1 s, ω=αt=3 rad/s. The required radial force is mω²r=9 N, while the given inward force is 5 N, so friction must provide 4 N radially. It also provides tangential force mαr=3 N. Thus f=√(4²+3²)=5 N=µmg, giving µ=0.5. Hence D.