Question

A cubical block is floating in a liquid with half of its volume immersed the liquid. When the whole system accelerated upwards with acceleration of $\frac{g}{3}$ the fraction of volume immersed in the liquid will be:

• A. $\frac{1}{2}$
• B. $\frac{3}{8}$
• C. $\frac{2}{3}$
• D. $\frac{3}{4}$

Answer 1

Answer: (A)

$\frac{1}{2}$

Volume of block immersed in liquid $V_{imm}=\frac{V_o}{2}$

where $V_o$ is the volume of block and $m$ is the mass of block.

Let $\rho$ be the density of liquid.

The weight of block is being balanced by buoyant force.

$⟹mg=V_{imm}\rho g$
$⟹mg=\frac{V_0}{2}\rho g$

When system is accelerated upwards, the effective weigh of body is $m(g+\frac{g}{3})$.

Thus effective weigh of body is $\frac{4mg}{3}$.

Hence $\frac{4}{3}mg=V_{imm}^{\prime }\rho g$
$⟹$ $V_{imm}^{\prime }=\frac{3}{4}{V}_0$

Thus fraction of volume immersed in liquid $=\frac{V_{imm}^{\prime }}{V_0}=$ $\frac{3}{4}$