A cylinder of mass m is suspended through two strings wrapped around it as shwon in figure . Find (a). the tension T in the string and (b). the speed o the cylinder as it falls through a distance h.

A cylinder of mass m is suspended through two strings wrapped around i

1.	A cylinder of mass m is suspended through two strings wrapped around it as shwon in figure . Find (a). the tension T in the string and (b). the speed o the cylinder as it falls through a distance h.
Answer» Solution :There is no horizontal force acting on the cylinder. The centre of MASS of the cylinder falls vertically downwards, The cylinder rolls down without slipping. Let the acceleration of the centre of mass of the cylinder be a. Then the ANGULAR acceleration is a `a=a/r` For the motion of the centre of mass `mg -2T =ma`.........(i) The torque acting on the cylinder is `tau = lalpha` `Tr + Tr -(1/2 mr^(2)) xx a/r` `2Tr =1/2mar, T = 1/4 ma` SUBSTITUTING in EQNS (i) `mg -1/2 ma = ma` `3/2 ma = mg, a=(2g)/3 = (2 xx 9.8)/3 = 6.53 m//s^(2)` `T = 1/4 ma = 1/4 xx (2 xx 2 xx 9.8)/3` Tension in the cords are 3.27 N each = 3.27 N