TS EAMCET · Physics · Mechanical Properties of Fluids
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 \(2 \mathrm{H}\)
- B \(4 \mathrm{H}\)
- C \(5 \mathrm{H}\)
- D \(3 \mathrm{H}\)
Answer & Solution
Correct Answer
(B) \(4 \mathrm{H}\)
Step-by-step Solution
Detailed explanation
From Boyle's law, \(P_1 V_1=P_2 V_2\) or, \(\rho\) ghv \(_1=(\rho g H+\) \(\rho g d) V_2\) \(\begin{aligned} & V_1=5 V \text { and } V_2=V, d=? \\ & \therefore H \times 5 V=(H+d) V \\ & \Rightarrow 5 H=H+d \therefore d=5 H-H=4 H\end{aligned}\)
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