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 tA and tB 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, h, vertically above X and reaches X in time tC. Choose the correct statement.

Question

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 tA and tB 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, h, vertically above X and reaches X in time tC. Choose the correct statement. (A) t C < t A < t C (B) tC =tA =tC (C) t C = t A < t C  (D) tB < tA=tC

Tardigrade Admin · Accepted Answer

Work done by gravity on A 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 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) (ii) t A = t B = t C Note: Correction in option option B should be t A = t B = t C

$t_{C} < t_{A} < t_{C}$

$t_{C} = t_{A} = t_{C}$

$t_{C} = t_{A} < t_{C}$

$t_{B} < t_{A} = t_{C}$

tC​<tA​<tC​

tC​=tA​=tC​

tC​=tA​<tC​

tB​<tA​=tC​

$t_{C} < t_{A} < t_{C}$

$t_{C} = t_{A} = t_{C}$

$t_{C} = t_{A} < t_{C}$

$t_{B} < t_{A} = t_{C}$