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 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, h, vertically above X and reaches X in time `t_C`. Choose the correct statement.

Options

A. `t_C lt t_A lt t_C`
B. `t_c=t_A=t_C`
C. `t_c=t_Altt_c`
D. `t_B lt t_A = t_C`

Answer

B

Explanation

Work done by gravity on A & B is same.
`therefore` Horizontal velocity of A = horizontal velocity of B as they leave the horizontal portion of the structure
`therefore t_A=t_B……(i)`
Also vertical velocity of A & vertical velocity of C when released are both zero
`therefore` They both will cover same vertical distance in same time
`therefore 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`