A body takes time `t` to reach the bottom oa a smooth inclined plane of angle `theta` with the horizontal. If the plane is made rought, time taken now is `2t`.The coefficient of friction of the rough surface is

Options

A. `(3)/(4) tan theta`
B. `(2)/(3) tan theta`
C. `(1)/(4) tan theta`
D. `(1)/(2) tan theta`

Answer

A

Explanation

`S = (1)/(2) at^(2)`
`:. t= sqrt((2S)/(a)` or `t prop (1)/(sqrt(a))`
`:. (t_(1))/(t_(2)) = ((a_(2))/(a_(2)))`
or `(t)/(2t) = ((g sin theta - mug cos theta)/(g sin theta ))`
On solving this equation , we get
`mu (3)/(4) tan theta`