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

Time in which plank and cylinder separate

Options

A. `1 sec`
B. `1.5 sec`
C. `2.5 sec`
D. `2 sec`

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.