Question

Q. The force required to just move a body up the inclined plane is double the force required to just prevent the body from sliding down the plane. The coefficient of friction is Mu. If theta is the angle of inclination of the plane, then tan theta is equal to
​​​​(1)mu
(2)3 mu
(3)2 mu
(4)0.5 mu

Answer 1

Retardation in upward motion
=g(sinθ+μcosθ)

∴ Force required just to move up
Fup=mg(sinθ+μcosθ)

Similarly for down ward motion a =g(sinθ−μcosθ)

∴ Force required just to prevent the body sliding down
Fdn=mg(sinθ−μcosθ)

According to problem
Fup=2Fdn
mg(sinθ+μcosθ)=2mg(sinθ−μcosθ)
sinθ+μ cosθ=2sinθ−2μ cosθ
3μcosθ=sinθ
tanθ=3μ