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Q.

A block starts moving up an inclined plane of inclination $30^{0}$ with an initial velocity of $v_{0}$ . It comes back to its initial position with velocity $v_{0} / 2$ .The value of the coefficient of kinetic friction between the block and the inclined plane is close to P/100. The nearest integer to P is ____

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answer is 35.

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Detailed Solution

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$\frac{1}{2} m v_{0}^{2} = \frac{m g s}{2} + μ m g \frac{\sqrt{3} s}{2} \frac{1}{2} \frac{m v_{0}^{2}}{4} = \frac{m g s}{2} - μ m g \frac{\sqrt{3} s}{2}$

For downward

$4 = \frac{1 + μ \sqrt{3}}{1 - μ \sqrt{3}} μ = \frac{\sqrt{3}}{5} = \frac{P}{100} \to \frac{1.732}{5} = \frac{P}{100} \to P = 1.732 \times 20 = 34.64 ≃ 35$

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A block starts moving up an inclined plane of inclination 300 with an initial velocity of v0. It comes back to its initial position with velocity v0/2.The value of the coefficient of kinetic friction between the block and the inclined plane is close to P/100. The nearest integer to P is ____