JEE Advanced 2014 · Paper 2 · Physics Q1

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PhysicsSingle correct+3 / -1Question 1 of 60

A tennis ball is dropped on a horizontal smooth surface. It bounces back to its original position after hitting the surface. The force on the ball during the collision is proportional to the length of compression of the ball. Which one of the following sketches describes the variation of its kinetic energy $K$ with time $t$ most appropriately? The figures are only illustrative and not to the scale.

K versus t: K starts at zero, rises along a concave-down curve to a flat maximum, dips sharply to zero and back at the collision, then falls along a concave-down curve to zero.

K versus t: K grows slowly at first then faster (concave-up rise) to a peak, dips sharply to zero and back during the collision, then decreases along a concave-up curve, mirror-symmetric about the collision.

K versus t: K rises along a concave-up curve, stays constant (a short flat top) during the collision, then decreases along a concave-up curve; no dip to zero.

K versus t: K increases linearly with t to a peak, dips sharply to zero and back at the collision, then decreases linearly to zero.

Answer and worked solution

Official answer: B

Free fall. Falling from rest, $v=gt$ , so $K=\tfrac12mg^2t^2$ : a parabola, concave up, starting at zero.

Collision. The force is proportional to compression (a spring-like contact), so the ball decelerates to rest and is pushed back out in a short time: $K$ dips to zero and returns to its peak value. The surface is smooth and the ball returns to the original height, so no energy is lost.

Rise. On the way up the motion is the time-reverse of the fall, so $K$ falls along the mirror-image concave-up curve.

Only sketch (B) has concave-up branches with a dip to zero at the collision.

(B)

Topics:Elastic and inelastic collisions Simple harmonic motion Motion graphs

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JEE Advanced 2014 · Paper 2, Physics question 1