Question

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 the body and plane is.

Answer 1

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 '$s$'

$s=\frac{1}{2}\left[g\sin \theta -\mu g\cos \theta \right]{\left(2t\right)}^2$ ....($1$)

On a smooth surface $a=g\sin \theta$

$s=\frac{1}{2}\left(g\sin \theta \right)t^2$ ....($2$)

Substitute ($2$) and ($1$) and solving

$\mu =1-\frac{1}{2^2}=\frac{3}{4}=0.75$