A particle is projected directly along a rough plane of inclination θ with velocity u . If after coming to the rest the particle returns to the starting point with velocity v , the coefficient of friction between the particle and the plane is

Step-by-step solution

u 2   =   2 as For upward motion u 2 = 2 ( μgcosθ + gsinθ ) s For downward motion v 2 = 2 ( gsinθ - μgcosθ ) s u 2 v 2 = μcosθ + sinθ sinθ – μcosθ u 2 sinθ - u 2 μcosθ = μv 2 cosθ + v 2 sinθ ( u 2 - v 2 ) sinθ = μ ( v 2 + u 2 ) cosθ μ = u 2 – v 2 u 2 + v 2 tanθ