A plank of length `20 m` and mass `1kg` is kept on a horizontal smooth surface. A cylinder of mass `1lg` is kept near one end of the plank. The coefficient of friction between the two surface is `0.5`. The plank is suddenly given a velocity `20 m//s` towards left

Which of the following statements is correct?

Options

A. pure rolling of cylinder takes place immediately
B. initially cylinder slips and then pure rolling begins
C. pure rolling never begins
D. there is no lose in kinetic energy during its entire motion.

Answer

B

Explanation

`f_(R)=(MR^(2))/2 alpha,f=5N,M=1 kg`,

`Ralpha=10 m//s^(2), a_(1)=f/M=5m//s^(2),a_(2)=5m//s^(2)`,
For `a_("contact")=a_(1), v_("contanct")=(a_(1)+Ralpha)t=15 t.....(1)`

From eqns. `(1)` and `(2)`we get
`t=1 sec`
Till the cylinder sllips on plank
`S_(rel)=u_(rel)+1/2a_(rel)t^(2),20xx1-1/2xx10xx1^(2)=15 m`
Velocity of plank when pure rolling begins
`v=20-5t=15 m//s`
Velocity of cylinder `a_(1)t=5m//s`
When pure rolling begins, friction force vanishes, velocity of plank and cylinder is constants. after pure rolling beings.