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A plank with a box on it at one end is g...

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.

A

0.6 and 0.5

B

0.5 and 0.6

C

0.4 and 0.3

D

0.6 and 0.6

Text Solution

Verified by Experts

The correct Answer is:
A
`mu_(s)` = coefficient of static friction = tan `30^(@) = (1)/(sqrt3)`
`implies mu_(s) = 0.58 ~~ 0.6`
Now , S = ut + `(1)/(2) at^(2)`
`implies 4 = (1)/(2) xx a (4)^(2)`
`implies a = 0.5 m//s^(2)`
Now , a = g `sin theta - mu_(k) g cos theta`
`implies mu_(k) = (g sin theta - a)/(g cos theta) = tan 30^(@) - (0.5)/(g cos 30^(@))`
`=0.58 - (0.5 xx 2)/(10 xx sqrt3)`
`=0.58 - 0.058 ~~ 0.5`
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