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J & K CET Medical J & K - CET Medical Solved Paper-2004

  • question_answer
    50.          A vessel, whose bottom has round holes with diameter of 1 mm is filled with water. Assuming that surface tension acts only at holes. Then, the maximum height to which the water can be filled in vessel without leakage is : (surface tension of water is \[75\times {{10}^{-3}}N/m\]and \[g=10\text{ }m/{{s}^{2}}\])

    A)  3 cm                                     

    B)  0.3 cm

    C)  3 mm                                   

    D)  3 m

    Correct Answer: A

    Solution :

                    For no leakage, \[h\rho g=\frac{2T}{R}\] \[\Rightarrow \]               \[T=\frac{Rh\rho g}{2}\] \[\Rightarrow \]               \[h=\frac{2T}{R\rho g}\] Given, \[T=75\times {{10}^{-3}}N/m,\text{ }g=10\text{ }m/{{s}^{2}},\] \[R=0.5\times {{10}^{-3}}m\]                 \[h=\frac{2\times 75\times {{10}^{-3}}}{(0.5\times {{10}^{-3}})(1000)10}\] \[\Rightarrow \]               \[h=30\times {{10}^{-3}}\times 100\,cm\]                 \[=3\,cm\]


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