The various forces acting on the body have been shown in the figure. The force on the body down the inclined plane in presence of friction µ is
F=mg‌sin‌θ−f=mg‌sin‌θ−µN=ma or a=g‌sin‌θ−µg‌cos‌θ Since block is at rest thus initial velocity u = 0 Therefore, time taken to slide down the plane t1=√
2s
a
=√
2s
g‌sin‌θ−µg‌cos‌θ
In absence of friction time taken will be t2=√
2s
g‌sin‌θ
Given :t1=2t2 t12=4t22 or
2s
g(sin‌g‌q−µ‌cos‌θ)
=2s×4g(sin‌θ) or sin‌θ=4‌sin‌θ−4µ‌cos‌θ orµ=