A box of mass `8 kg ` placed on a rough inclined plane of inclened `theta` its downward motion can be prevented by applying an upward pull `F` and it can be made to slide upward appliying a force `2F` .The coefficient of friction between the box and the inclined plane is

Options

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

Answer

A

Explanation

(a) `F= mg sin theta -mu mg cos theta`……………(i)
2F= mg sin theta+mu mg cos theta`………….(ii)
`implies 2 mg sin theta-2 mu mg cos theta= mg sin theta+ mu mg cos theta`
`therefore " " mu (1)/(3) tan theta`