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Q.

The time taken by a body to slide down a rough $45^{o}$ inclined plane is twice that required to slide down a smooth $45^{o}$ inclined plane. The coefficient of kinetic friction between the object and rough plane is $\frac{3}{x}$ . The value of $x$ is____________

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Detailed Solution

$t = \sqrt{\frac{2 S}{a}} \propto \frac{1}{\sqrt{a}}$

$∴ \frac{t_{1}}{t_{2}} = \sqrt{\frac{a_{2}}{a_{1}}}$

$\frac{2}{1} = \sqrt{\frac{g \sin θ}{g \sin θ - μ_{K} g \cos θ}} = \sqrt{\frac{1}{1 - μ_{K}}}$

As, $\sin θ = \cos θ a t 45^{o}$

On solving the above equation, we get $μ_{K} = \frac{3}{4}$

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The time taken by a body to slide down a rough 45o inclined plane is twice that required to slide down a smooth 45o inclined plane. The coefficient of kinetic friction between the object and rough plane is 3x. The value of x is____________