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J & K CET Engineering J and K - CET Engineering 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 \[1\text{ }atm=1\times {{10}^{5}};\] \[\rho \]p water\[={{10}^{3}}\])

    A)  \[9.6\text{ }m\]  

    B)  \[7.5\text{ }m\]   

    C)  \[4.4\text{ }m\]  

    D)  \[3.2\text{ }m\]

    E) Not Available

    Correct Answer: E

    Solution :

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


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