A block is sliding down on an inclined plane of slope θ and at an instant t=0 this block is given an upward momentum so that it starts moving up on the inclined surface with velocity u. The distance (S) travelled by the block before its velocity become zero, is ____ .
(g = gravitational acceleration)

Solution

Physics sir · 3 steps

On the way up, only the component of gravity along the incline slows the block, and that is g sin θ.

1. Forces along incline. Take the incline as smooth, as the options assume. Split gravity into two parts: mg cos θ into the surface, balanced by the normal force, and mg sin θ along the surface, pointing down the slope.
2. Deceleration. While the block moves up, the force mg sin θ acts against the motion. By Newton's second law the retardation is a = (mg sin θ)/m = g sin θ, and it stays the same the whole way up.

   v² = u² - 2aS ⇒ 0 = u² - 2g sin θ S

3. So. S = u²/(2g sin θ), which is option (c).

The idea to keep. On a smooth incline, the acceleration along the surface is always g sin θ, whether the block goes up or down. The cos θ part only presses the block into the surface.

Answer from the NTA final answer key. Solution by PrepWiser.