A plank w ith a box on it atone end is gradually raised about the other end . As the ang le of in clin ation with the horizontal reaches `30^(@)`, the box starts to slip and slides 4.0 m down the plan k in 4.0s. The coefficients of static and k inetic 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

Coefficient of static friction `mu_(s ) = tan 30^(@)`
`= (1)/(sqrt(3)) = 0.577 = 0.6`
Now acceleration a= g sin `30^(@) - mu_(k) cos 30^(@)`
`=(g ) /(2) - (sqrt(3mu_(kg)))/(2)`
Now in equation of motion S= `v_(0) t+ (1)/(2) at^(2)`
`(8)/(16) = (g ) /(2) - (sqrt(3mu_(kg )))/(2 )`
`1= 9.8 - 1732 xx mu_(g ) xx 9.8`
`mu_(k ) = (8.8)/( 16.97) = 0 .518`
`mu_(k ) = 0.5`