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  • The temperature of an air bubble, while giving from bottom to surface of a lake remains constant, but its diameters is doubled. If pressure on the surface <img alt="=h" src="https://

The temperature of an air bubble, while giving from bottom to surface of a lake remains constant, but its diameters is doubled. If pressure on the surface =h metre of \mathrm{Hg} col and relative density of mercury is \rho , then depth of the lake is :

 

Option: 1

2 \mathrm{sh} metre


Option: 2

4 \mathrm{sh} metre


Option: 3

7 \mathrm{sh} metre


Option: 4

9 \mathrm{gh} metre


Answers (1)

best_answer

As temperature remains constant , therefore according to Boyle'sLaw,

P_{1} V_{1}=P_{2} V_{2} \text { where }

V_{1}=\frac{4}{3} \pi R_{1}^{3} at the bottom.

V_{2}=\frac{4}{3} \pi R_{2}^{3}\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} \\ & \begin{array}{l} P_{2}=P_{1} \frac{v_{1}}{v_{2}}=\frac{P_{1}}{8} \quad \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} \quad H=7 h \frac{d_{m}}{d_{\omega}}=7 h \rho \end{array} \end{aligned}

option c is correct.

 

Posted by

manish

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