Question

# A block kept on a rough inclined plane, as shown in the figure, remains at rest upto a maximum force $$2 \,N$$ down the inclined plane. The maximum external force up the inclined plane that does not move the block is $$10 \,N$$. The coefficient of static friction between the block and the plane is :                  [Take $$g = 10 \,m/s^2$$]

A
23
B
32
C
34
D
14

Solution

## The correct option is D $$\dfrac{\sqrt{3}}{2}$$From the free body diagram$$\sum F = 0$$$$2 + mg \,\sin 30 = \mu mg \,\cos 30^o$$.............................$$(i)$$$$10 = mg \,\sin \,30 + \mu \,mg \,\cos \,30^o$$.....................$$(ii)$$Adding eq $$(i)$$ and $$(ii)$$, we get$$12 = 2\mu \,mg \,\cos \,30$$$$6 = \mu \,mg \,\cos \,30$$.......................................$$(iii)$$$$4 = mg \,\sin \,30$$.............................................$$(iv)$$From eqn $$(iii)$$ and $$(iv)$$, we get$$\dfrac{3}{2} = \mu \times cot 30^0$$$$\dfrac{3}{2} = \mu \times \sqrt{3}$$$$\mu = \dfrac{\sqrt{3}}{2}$$Physics

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