Question

A uniform solid cylinder of mass 5kg and radius 0.1m is resting on a horizontal platform (parallel to the x-y plane) and is free to rotate about its axis along the y-axis the platform is given a motion in the x direction given by x=0.2 cos (10t) m if there is no slipping then maximum torque acting on the cylinder during its motion is
A. `0.2 N-m`
B. `2.0 N-m`
C. `5.0N-m`
D. `10.0N-m`

Answer 1

Correct Answer - C
`Ialpha = ((MR^(2))/2)xx(a/R)`
`a=(d^(2)x)/dt^(2)= -0.2xx 100cos(10t)=-20cos(10t)`
`alpha=a/R=-200cos(10t)`
`=-(5xx(0.1)^(2))/2 xx200cos(10t)=-5/2xx2xxcos(10t)=-5cos(10t)`
`t_(max)=5Nxxm`