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# Starting from rest a body slides down a $45^{\circ}$ inclined plane in twice the time it takes to slide down the same distance in the absence of friction. The coefficient of friction between body and plane is

$(a)\;0.33 \quad (b)\;0.75 \quad (c)\;0.25 \quad (d)\;0.80 N$

on a rough surface acceleration of a body down a plane
$a=(g \;sin \theta-\mu g \cos \theta)$
'2t' is time taken to go down a rough inclined plane of length 's'
't' is time taken to go down a smooth inclined plane of length 's'
$s=\large\frac{1}{2}$$[g \sin \theta -\mu g \cos \theta](2t)^2-----(1) On a smooth surface a=g \sin \theta s= \large\frac{1}{2}$$(g \sin \theta)t^2$-----(2)
Substituting (2) in (1) and solving
$\mu =1- \large\frac{1}{2^2}$
$\mu =\large \frac{3}{4}$
$\qquad=0.75$
Hence b is the correct answer.
edited May 27, 2014