A plank with a box on it at one end is gradully raised about the other end. As the angle of inclination with the horizntal reaches `30^(@)` , the box starts to slip and slide `4.0m` down the plank in `4.0s` . The coefficients of static and knitic 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

When start sliding `mu_(s)=Tan theta=Tan 30^(@)`
`mu_(s)=0.58~~0.6`
After slipping
`S=ut+(1)/(2)at^(2)`
`4=(1)/(2)xxaxx16`
`a=(1)/(2)`
`a=g(sin 30-mu_(k)cos 30^(@))`
`mu_(k)=0.52~~0.5`
`=m_(2)(g-(m_(2)g-mum_(1)g)/(m_(1)+m_(2)))`
`m_(g)g((m_(1)+m_(2)-m_(2)+mum_(1))/(m_(1)+m_(2)))`
`=(m_(1)m_(2)g(1+mu))/(m_(1)+m_(2))`