A fixed pulley of radius 20 cm and moment of inertia 0.32 kg·m² about its axle has a massless cord wrapped around its rim. A mass M of 2 kg is attached to the end of the cord. The pulley can rotate about its axis without any friction. The acceleration of the mass M is:- (Assume g = 10 m/s²)

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G1 Physics · Accepted Answer

For the falling mass, Mg-T=Ma. For the pulley, TR=Iα=I(a/R), so T=Ia/R². Thus a=Mg/(M+I/R²)=20/(2+0.32/0.04)=2 m/s². Hence C. Use I=∫r²dm. For a shifted parallel axis use I=I about CM+Md²; for a plane lamina use I about z-axis=Iₓ+Iᵧ..