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A solid cylinder of length L and radius R has a weight W. Two cords are wrapped around the cylinder, one near each end, and the cord ends are attached to hooks on the ceiling. The cylinder is held horizontally with the two cords exactly vertical and is then released (Fig). Find (a) the tension in each cord as they unwind and (b) the linear acceleration of the cylinder as it falls.
ma=mg-2T --------------(1)As the tension on both the cords are same.Net torque,=1+2=2rT=Iα2rT=1/2(mr2)a/r=1/2mraT=1/4(ma)(1) => ma=mg-2(1/4(ma)) a=2/3gT=1/4(m(2/3g))T=1/6(mg) =W/6
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