A block is projected upwards along a rough inclined plane of angle 60^ . It momentarily comes to rest and then slides back down to its starting point. If the time taken by the block to slide down is twice the time taken to slide up, the coefficient of kinetic friction between the block and the incline is :

Step-by-step solution

Let the distance moved along the incline be d . During the upward motion, friction acts downwards. The retardation is: a_ up = g( 60^ + _k 60^ ) Using d = 1 2 a_ up t_ up ^2 (analyzing the ascent in reverse from the highest point where velocity is zero). During the downward motion, friction acts upwards. The acceleration is: a_ down = g( 60^ - _k 60^ ) Using d = 1 2 a_ down t_ down ^2 . Equating the two expressions for d : 1 2 a_ up t_ up ^2 = 1 2 a_ down t_ down ^2 a_ up a_ down = ( t_ down t_ up )^2 Given t_ down