A ball `P` moving with a speed of `v ms^-1` collides directly with another identical ball `Q` moving with a speed `10 ms^-1` in the opposite direction. P comes to rest after the collision. If the coefficient of restitution is 0.6, the value of v is

Options

A. `30 ms^-1`
B. `40 ms^-1`
C. `50 ms^-1`
D. `60 ms^-1`

Explanation

Force required to move a body upwards on a rough inclined plane is,
`F_1 = mg(sintheta + mucostheta)` .....(1)
Force required to prevent the body from sliding down the plane is,
`F_2= mg(sintheta-mucostheta)` ....(2)
`F_1=2F_2`
`implies mg(sintheta-mucostheta)=2mg(sintheta-mucostheta)`
`implies sintheta+mucostheta=2(sintheta-mucostheta)`
` sintheta+mucostheta=2sintheta-2mucostheta`
`impliessintheta=3mucosthetaimpliesmu=1/3tantheta`
`impliesmu=1/3tan60^0=1/3(sqrt3)=1/sqrt3`