An ideal string is wrapped several times on a solid cylinder of mass 4kg and radius 1m. The pulleys are ideal and the surface between block and ground is smooth. If the torque acting on the cylinder is $\frac{10 x}{9}$ N-m, then find the value of x.

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answer is 8.

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Detailed Solution

FBD of cylinder and block are as shown by Newton’s laws
40 – 2T – f_s = 8a (1)
T – f_s = 4a/2 (2)
Subtracting equation (2) from equation (1)
40 – 3T = 6a
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T = (40 – 6a)/3
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