question_answer

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 \[{{30}^{o}},\] the box starts to slip and slides m down the plank in 4.0 s. The coefficients of static and kinetic friction between the box and the plank will be, respectively                    [NEET 2015 (Re)]

A)       0.6 and 0.6

B) 0.6 and 0.5

C) 0.5 and 0.6

D) 0.4 and 0.3

Correct Answer: B

Solution :

Given a plank with a box on it one end is gradually raised about the end having angle of  Inclination, the box starts to slip and slides down 4 m the Plank m 4 s as shown in figure.

The coefficient of static friction,

\[{{\mu }_{s}}=\tan {{30}^{{}^\circ }}=\frac{1}{\sqrt{3}}=0.6\]

So, distance covered by a plank,

\[s=ut+\frac{1}{2}a{{t}^{2}}\]

Here, \[u=0\] and  \[a=g\,(\sin \theta -\mu \,\cos \theta )\]

\[\therefore \]      \[4=\frac{1}{2}g(\sin 30-{{\mu }_{k}}\cos 30){{(4)}^{2}}\]

\[\Rightarrow \]   \[0.5=10\times \frac{1}{2}-{{\mu }_{x}}\times 10\times \frac{\sqrt{3}}{2}\]

\[\Rightarrow \]   \[5\sqrt{3}{{\mu }_{k}}=45\Rightarrow {{\mu }_{k}}=0.51\]

Thus, coefficient of kinetic friction between the box and the plank is 0.51.