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KVPY2020PhysicsMotion in One Dimension

Three balls, A , B and C , are released and all reach the point X (shonw in the figure). Balls A and B are released from two identical structures, one kept on the ground and the other at height, h , from the ground as shown in the figure. They take time t A and t B respectively to reach X (time starts after they leave the end of the horizontal portion of the structure). The ball C is released from a point at height,

Options

  1. At C < t A < t C
  2. Bta = tb = tc
  3. Ct C = t A < t C
  4. Dt B < t A = t C

Correct answer

B. ta = tb = tc

Step-by-step solution

Work done by gravity on A and B is same. ∴ Horizontal velocity of A = horizontal velocity of B as they leave the horizontal portion of the structure. ∴   t A = t B … ( i ) Also vertical velocity of A and vertical velocity of C when released are both zero ∴ They both will cover same vertical distance in same time. ∴   t A = t C . . . ( ii ) From ( i ) and ( ii ) t A = t B = t C Note : Correction in option option B should be t A = t B = t C

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