A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches `30^(@)` , the box starts to slip and slide `4.0m` down the plank in `4.0s` . The coefficients of static and kinetic friction between the box and the plank will be, respectively.

Options

A. `0.4` and `0.3`
B. `0.6` and `0.6`
C. `0.6` and `0.5`
D. `0.5` and `0.6`

Answer

C

Explanation

Coeffcient of static friction,
`mu_(s)=tantheta30^(@)=(1)/sqrt(3)=0.6`
Acceleration of the box, `a=gsin30^(@)-mu_(k)gcos30^(@)`
Using, `S=ut+(1)/(2)at^(2)`
implies `4=(1)/(2)[(g)/(2)-(mu_(k)gsqrt(3))/(2)]xx16` implies `mu_(k)=0.5`