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 $t_{A}$ 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.

• A. $t _{C} < t _{ A }< t _{C}$
• B. $t_{C} =t_{A} =t_{C}$
• C. $t _{ C }= t _{ A }< t _{ C }$
• D. $t_{B} < t_{A}=t_{C}$

Answer 1

Answer: (B)

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
$t _{ A }= t _{ B }= t _{ C }$