Blocks A and B of masses 4 kg and 2 kg are connected by a light string over a disc C of mass 40 kg and radius 0.1 m. The system is released from rest and the string does not slip. The number of revolutions made by the disc after 10 s is n × 10³/(26π). Find n.

Question

G1 Physics · Accepted Answer

Let downward acceleration of the 4 kg block be a. For the two blocks: 4g-T₁=4a and T₂-2g=2a. For the disc, (T₁-T₂)R=Iα with I=½(40)R² and α=a/R, so T₁-T₂=20a. Combining gives a=10/13 m/s². Therefore α=100/13 rad/s². In 10 s, θ=½αt²=5000/13 rad, so revolutions = θ/(2π)=5000/(26π)=5×10³/(26π). Hence n=5.