A box when dropped from a certain height reaches the ground with a speed ν. When it slides from rest from the same height down a rough inclined plane inclined at an angle `45^(@)` to the horizontal, it reaches the ground with a speed `ν//3`. The coefficient of sliding friction between the box and the plane is (acceleration due to gravity is `10 ms^(-2))`

Options

A. `8//9`
B. `1//9`
C. `2//3`
D. `1//3`

Answer

A

Explanation

Case-1
`v = sqrt(2gh)`
Case-2
`Delta U + Delta kE = w_(f)`

`-mgh+(1)/(2)m((2gh)/(9))=-mumgh" "mu =(8)/(9)`