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A mass m slides down a fixed plane inclined at angle $α$ to the horizontal. Find the distance that it will move on the horizontal plane after covering the entire length of the inclined plane. The height of the inclined plane is h and the co-efficient of friction over both surfaces is $μ$

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$h [\frac{1}{μ} - \cot α]$

$h [1 - \frac{1}{\tan α}]$

$h [\frac{1}{μ} - 1]$

$h [μ - \frac{1}{Tan α}]$

answer is A.

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Detailed Solution

Block starts from A and cones to rest again at C Along the path, loss in GPE= work done against friction on inclined plane and horizontal plane

$m g h = W_{A B} + W_{B C}$

$m g h = (μ m g \cos α) A B + (μ m g) B C$

$m g h = μ m g \cos α (\frac{h}{\sin α}) + μ m g l$

$h - μ h \cot α = μ l$

$l = h [\frac{1}{μ} - \cot α]$

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