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. |
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