if the minimum horizontal force required to drag a heavy body on a rough horizontal surface be n times its magnitude, when it be inclined to the horinzontal at the angle of friction. find coefficient of friction.

The free body diagram is shown below:

on balancing forces we have

F and R are forces and u (=tan x) is coeff of friction

N₁ =mg  and F = f₁ = uN₁ =umg

N₂ = mg.cosx

f₂=uN₂=umgcos x

R=f₂+mgsinx

R = mg(u cosx+sinx)

also given :  R = nF

so,  nu.mg = mg(u cosx+sinx)

also tanx =u

so , n = 2 (1+ u² )^-1/2

so coeff of friction: u = (1 -(4/n²) )^1/2

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