JEE Main & Advanced Sample Paper JEE Main Sample Paper-26

  • question_answer
    A large open tank has two holes in its wall. One is a square hole of side a at a depth of \[x\] from the top and the other is a circular hole of radius r at a depth \[4x\] from the top. When the tank is completely filled with water, the quantities of water flowing out per second from both holes are the same. Then r is equal to :

    A)  \[2\pi a\]                                  

    B)  a

    C)  \[\frac{a}{2\pi }\]                                 

    D)  \[\frac{a}{\sqrt{2\pi }}\]

    Correct Answer: D

    Solution :

    Rate of flow \[=\frac{d(Volume)}{dt}\,=Area\,\times \,\] (Velocity of flow) \[{{v}^{2}}=2gh\Rightarrow \,{{a}^{2}}\,\sqrt{2gh}\,=\pi {{r}^{2}}\sqrt{2g\mu x}\times 2\] \[\Rightarrow \,r=\frac{a}{\sqrt{2\pi }}\]

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