A rough inclined plane makes an angle 30° with horizontal and a block weighing 10 N on this inclined plane slides down with uniform velocity. How much horizontal force should be applied on the block so that it slides up the inclined plane with uniform velocity?

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A rough inclined plane makes an angle 30° with horizontal and a block weighing 10 N on this inclined plane slides down with uniform velocity. How much horizontal force should be applied on the block so that it slides up the inclined plane with uniform velocity?

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$20 \sqrt{3} N$

$10 \sqrt{2} N$

$20 N$

$10 \sqrt{3} N$

answer is B.

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Detailed Solution

$\begin{array}{l} From given condition, mg sinθ = μmg cosθ \\ \Rightarrow μ = tanθ = \frac{1}{\sqrt{3}} \\ Let horizontal force applied is F, then \\ Fcosθ = mgsinθ + μR \\ R = mgcosθ + Fsinθ \\ \Rightarrow F = 10 \sqrt{3} N \end{array}$