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CMC Medical CMC-Medical VELLORE Solved Paper-2015

  • question_answer
    The water has surface tension 0.075 \[N{{m}^{-1}}\] white its density is 1000\[kg{{m}^{-3}}\]. There is an air bubble of radius 1.0 mm inside the water at depth 10 cm below the free surface. The difference between pressure inside the bubble and the atmospheric pressure is

    A)  983 Pa                 

    B)  1070 Pa

    C)  1083 Pa                               

    D)  1130 Pa

    E)  1134 Pa

    Correct Answer: D

    Solution :

                    Let the atmospheric pressure is\[{{p}_{0}}.\] The just outside the bubble and inside the water \[p={{p}_{0}}+\rho \,gh\] Also, pressure inside the bubble \[p=p+\frac{2\,s}{r}={{p}_{0}}+h\,\rho \,g+\frac{2s}{r}\] \[\Rightarrow p-{{p}_{0}}=(10\,cm)\,(1000\,kg{{m}^{-3}})\,(9.8\,m{{s}^{-2}})\]\[+\frac{2\times 0.075\,N{{m}^{-1}}}{10\times {{10}^{-3}}m}\] \[=980\,N{{m}^{-2}}+150\,N{{m}^{-2}}=1130\,Pa\]


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