JEE Main 2023 — Mechanical Properties of Fluids Question with Solution

The pressure at the bottom of the lake can be calculated as follows:

$\begin{array}{rcl}{P}_{bottom}& =& P_0 + \rho gh\\ & =& \left({10}^5+1000 \times 10 \times 40\right) \mathrm{Pa}\\ & =& 5\times {10}^5 \mathrm{Pa} \end{array}$

As the temperature of water remains constant, it can be written that

$P_{\mathrm{bottom}}{V}_{\mathrm{bottom}}=P_{\mathrm{top}}{V}_{\mathrm{top}} ...\left(1\right)$

Substitute the values of the known parameters into equation (1) to calculate the required volume of the bubble when it reaches the surface.

$\begin{array}{rcl}5\times {10}^5\times 1& =& 1\times {10}^5\times V_{\mathrm{top}}\\ & \Rightarrow & V_{\mathrm{top}}=\frac{5\times {10}^5\times 1}{1\times {10}^5} {\mathrm{cm}}^3\\ & =& 5 {\mathrm{cm}}^3\end{array}$