Mechanical Properties of Fluids - Result Question 5
5. In rising from the bottom of a lake, to the top, the temperature of an air bubble remains unchanged, but its diameter gets doubled. If $h$ is the barometric height (expressed in $m$ of mercury of relative density $\rho$ ) at the surface of the lake, the depth of the lake is
[1994]
(a) $8 \rho m$
(b) $7 \rho m$
(c) $9 \rho m$
(d) $12 \rho h$
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Answer:
Correct Answer: 5. (b)
Solution:
- (b) $(h \rho g+H \times 1 \times g) \frac{4}{3} \pi r^{3}=h \rho g \times \frac{4}{3} \pi(2 r)^{3}$
This gives $H=7 h \rho$
