Q133 / 160 · TS EAMCET 2023 (14 May Shift 2) · Physics

When a large bubble rises from the bottom of a lake to the surface, the volume of the bubble becomes 5 times its volume at the bottom of the lake. If $\mathrm{H}$ is the atmospheric pressure expressed in terms of water column height, then the depth of the lake is (The temperature of the water in the lake is same at all points)

  • A
    $2 \mathrm{H}$
  • Correct answer
    B
    $4 \mathrm{H}$
  • C
    $5 \mathrm{H}$
  • D
    $3 \mathrm{H}$

Solution

From Boyle's law, $P_1 V_1=P_2 V_2$ or, $\rho$ ghv $_1=(\rho g H+$ $\rho g d) V_2$ $\begin{aligned} & V_1=5 V \text { and } V_2=V, d=? \\ & \therefore H \times 5 V=(H+d) V \\ & \Rightarrow 5 H=H+d \therefore d=5 H-H=4 H\end{aligned}$

Hence, the correct answer is option: 'B'.

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