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  • The temperature of an ais bubble, while rising from bottom to surface of a lake remains constant, but its diameter is doubled. If pressure on the surface <img alt="=h ~metre" src="https://entr

The temperature of an ais bubble, while rising from bottom to surface of a lake remains constant, but its diameter is doubled. If pressure on the surface =h ~metre of Hg col and relative density of mercury is \rho, then the depth of lake is-

Option: 1

2 \rho \mathrm{h} ~metre


Option: 2

4\rho \mathrm{h} ~metre


Option: 3

7 \rho \mathrm{h} ~metre


Option: 4

9 \rho \mathrm{h}~ metre


Answers (1)

best_answer

As temperatiac remains constant, therefore, according to Boyle's law -
P_1 V_1=P_2 V_2; where

V_1=\frac{4}{3} \pi R_1^3

At the bottom

\begin{aligned} V_2&=\frac{4}{3} \pi R_2^3\\ \text { or } \frac{4}{3} \pi\left(2 R_1\right)^3&=8 V_1 \\ P_2&=P_1 \frac{V_1}{V_2}=\frac{P_1}{8} \\\therefore h\left(d_m\right) g&=\left(H d_\omega+h d_m\right) \frac{g}{8} \\ H d_\omega&=7 h d_m \\ H&=7 h \frac{d_m}{d_\omega}=7 h \rho \end{aligned}
 

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Shailly goel

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