JEE Main & Advanced Physics Fluid Mechanics, Surface Tension & Viscosity / द्रव यांत्रिकी, भूतल तनाव और चिपचिपापन Question Bank Pressure Difference

  • question_answer
    The volume of an air bubble becomes three times as it rises from the bottom of a lake to its surface. Assuming atmospheric pressure to be 75 cm of Hg and the density of water to be 1/10 of the density of mercury, the depth of the lake is                                 [AMU 1995]

    A) 5 m     

    B)  10 m

    C)             15 m   

    D)  20 m

    Correct Answer: C

    Solution :

                    \[{{P}_{1}}{{V}_{1}}={{P}_{2}}{{V}_{2}}\]Þ \[({{H}_{Hg}}{{\rho }_{Hg}}+{{H}_{W}}{{\rho }_{W}})V={{H}_{Hg}}{{\rho }_{Hg}}\times 3V\] Þ \[{{H}_{Hg}}{{\rho }_{Hg}}+{{H}_{W}}\frac{{{\rho }_{Hg}}}{10}=3{{H}_{Hg}}{{\rho }_{Hg}}\] Þ\[{{H}_{W}}=2{{H}_{Hg}}\times 10\]\[=\frac{2\times 75\times 10}{100}=15m\]


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