The upper half of an inclined plane with inclination `phi` is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for the lower half is given by

Options

A. `tan phi`
B. `2 tan phi`
C. `2 cos phi`
D. `2 sin phi`

Answer

B

Explanation

Refer to figure. In the journey over the upper half of incline, `upsilon^(2)- u^(2)=2 as `
`upsilon^(2)-0=2 ( g sin phi)(s)/(2)= g sin phi. S`
In the journey over the lower half of incline
`upsilon^(2)-u^(2) = 2 a s `
`o-g sin phi.s=2 g ( sin phi - mu cos phi ) ( s)/(2)`
`- sin phi = sin phi - mu cos phi`
`mu= (2 sin phi)/( cos phi)=2 tan phi`