JEE MAINS PHYSICS QUESTION SEPTEMBER 2020
Answers
A ball is dropped vertically from a height d above the ground. it hits the ground and bounces up vertically to a height d/2. neglecting subsequent motion and air resistance. its velocity v varies with the height h ground as ...
solution : as the ball is dropped vertically from a height d above the ground.
velocity before striking the ground, v = √2gd
⇒v² = 2gd
differentiating both sides w.r.t d we get,
2v dv/d(d) = 2g
⇒dv/d(d) = g/v
here it is clear that slope of graph of velocity and distance is inversely proportional to velocity. means higher the value of v, higher will be the value of slope. at highest point, velocity becomes zero. so slope will be infinite i.e., tan90° = ∞, it means graph will be perpendicular on axis of height.
but first time v = -√2gd [ negative sign indicates body moves downward ]
and 2nd time v' = √(2gd/2) = √gd [positive sign indicates body moves upward ]
from above explanation only option (1) looks like an appropriate graph.
Therefore the correct option is (1)