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An ideal string is wrapped several times on a solid cylinder of mass 4 kg and radius 1 m. The pulleys are ideal and the surface between block and ground is smooth. Cylinder rolls without slipping on the block. 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

$40 - T - f = 8 a_{1}$

$f - \frac{T}{2} = 4 a_{2}$

$(f + \frac{T}{2}) R = \frac{4 R^{2}}{2} α$

$a_{2} + R α = a_{1}$

$R α - a_{2} = 2 a_{1}$

$α = \frac{40}{9}$

$τ = \frac{4 (1) α}{2} = \frac{80}{9}$

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