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Question

A small solid ball of density ρ is held inside at point A of a cubical container of side L, filled with an ideal liquid of density 4ρ as shown in the figure. Now, if the container starts moving with constant acceleration a horizontally and the ball is released from point A simultaneously, then
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A
For ball to hit the top of container at end Q,a=3 g
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B
For ball to hit the top of container at end Q,a=2 g
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C
Ball hits the top of container at end Q after a time t=L3g
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D
Ball hits the top of container at end Q after a time t=2L3g
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Solution

The correct options are
B For ball to hit the top of container at end Q,a=2 g
C Ball hits the top of container at end Q after a time t=L3g
Let the acceleration is a
ay=4ρVgVρgVρ=3g
ax=4ρVaVρaVρ=3a
At Y-direction:
L2=12×3g×t2
t2=L3g
At X-direction:
L=12×3a×t2
t2=2L3a
Comparing these two we get:a=2g
So, t=L3g

The correct answers are B and C

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