A solid cylinder of mass 50 kg and radius 0.5 m is free to rotate about the horizontal axis . A massless string is wound around the cylinder with one end attached to it and other hanging freely . Tension in the string required to produce an angular acceleration of 2 revolutions s^(-2) is

A solid cylinder of mass 50 kg and radius 0.5 m is free to rotate abou

1.	A solid cylinder of mass 50 kg and radius 0.5 m is free to rotate about the horizontal axis . A massless string is wound around the cylinder with one end attached to it and other hanging freely . Tension in the string required to produce an angular acceleration of 2 revolutions s^(-2) is
Answer» 25 N 50 N 78.5 N 157 N Solution :Here , MASS of the cylinder , M = 50 kg Radius of the cylinder , R = 0.5 m Angular acceleration , `ALPHA = 2 rev s^(-2)` `= 2 xx 2pi rad s^(-2) = 4pi rad s^(-2)` Torque , `tau = TR` Moment of inertia of the solid cylinder about its AXIS , `I = (1)/(2) MR^(2)` `therefore` Angular acceleration of the cylinder , `alpha = (tau)/(I) = (TR)/((1)/(2) MR^(2))` `T = (MR alpha)/(2)= (50 xx 0.5 xx 4pi)/(2) = 157 N`