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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 $$g = 10 \,m/s^2$$]
1332128_e78cc841711f45f493a06c36462ea8dd.PNG


A
23
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B
32
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C
34
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D
14
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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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