J & K CET Medical J & K - CET Medical Solved Paper-2014

  • question_answer
    If the pressure at half of the lake is equal to 1/3 pressure at the bottom of the lake, what is the depth of the lake? (Assume\[g=10\text{ }m/{{s}^{2}}\]and 1 aim\[=1\times {{10}^{5}};\text{ }\rho \]water\[={{10}^{3}}\])

    A)  9.6 m  

    B)  7.5 m   

    C)  4.4 m  

    D)  3.2 m

    E)  None of the Above

    Correct Answer: E

    Solution :

     According to equations, \[p\left( \frac{h}{2} \right)=\frac{1}{3}p(h)\] \[\left( 1\,atm+\rho g\frac{h}{2} \right)=\frac{1}{2}\left( 1\,atm+\rho gh \right)\] \[3\,atm+\frac{3}{2}\rho gh=1\,atm+\rho gh\] \[2\,atm=\rho gh-\frac{3}{2}\rho gh\] \[2\,atm=-\frac{\rho gh}{2}\] \[2\times {{10}^{5}}=-\frac{{{10}^{3}}\times 10\times h}{2}\] \[h=-40m\]


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