Question

A small solid ball of density $\rho$ is held inside at point $A$ of a cubical container of side $L$, filled with an ideal liquid of density $4\rho$ 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

• A. For ball to hit the top of container at end $Q,a=3g$
• B. For ball to hit the top of container at end $Q,a=2g$
• C. Ball hits the top of container at end Q after a time $t=\sqrt{\frac{L}{3g}}$
• D. Ball hits the top of container at end Q after a time $t=\sqrt{\frac{2L}{3g}}$

Answer 1

Answer: (B), (C)

The correct options are
B For ball to hit the top of container at end $Q,a=2g$
C Ball hits the top of container at end Q after a time $t=\sqrt{\frac{L}{3g}}$

Let the acceleration is $a$

$a_y=\frac{4\rho Vg-V\rho g}{V\rho }=3g$

$a_x=\frac{4\rho Va-V\rho a}{V\rho }=3a$

At Y-direction:

$\frac{L}{2}=\frac{1}{2}\times 3g\times t^2$

$t^2=\frac{L}{3g}$

At X-direction:

$L=\frac{1}{2}\times 3a\times t^2$

$t^2=\frac{2L}{3a}$

Comparing these two we get:$a=2g$

So, $t=\sqrt{\frac{L}{3g}}$

The correct answers are $B$ and $C$