A cylinder of mass m is placed on the edge of a long plank of same mass kept on the smooth horizontal surface, where `mu` the is the coefficient of friction between cylinder and plank. The cylinder is given an impulse at t=0 which impacts it is velocity `V_(0)`. find the time in which pure rolling starts.

Options

A. `V_(0)//2mug`
B. `V_(0)//4 mug`
C. `V_(0)2 sqrt(2) mu g`
D. `V_(0)//4 sqrt(2) mu g`

Answer

2

Explanation

Acceleration of plank, `=ap=mug`
`alpha_(c)=(mu mgR)/((mR^(2)//2))`

`=(2mug)/R`
For pure rolling after t,
`V_(P)=V_(C)-R omega_(c)`
`alpha pt =(V_(0) -a_(C)t)-Ralpha_(C) t`
or `mug t =(V_(0) - mu g t ) -2 mu g t `
`t=V_(0) //4g`