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JEE Main & Advanced Physics Fluid Mechanics, Surface Tension & Viscosity / द्रव यांत्रिकी, भूतल तनाव और चिपचिपापन Question Bank Critical Thinking

  • question_answer
    A cylinder containing water up to a height of 25 cm has a hole of cross-section \[\frac{1}{4}c{{m}^{2}}\] in its bottom. It is counterpoised in a balance. What is the initial change in the balancing weight when water begins to flow out

    A)             Increase of 12.5 gm-wt    

    B)             Increase of 6.25 gm-wt    

    C)             Decrease of 12.5 gm-wt

    D)             Decrease of 6.25 gm-wt

    Correct Answer: C

    Solution :

                       Let A = The area of cross section of the hole                    v = Initial velocity of efflux                    d = Density of water, Initial volume of water flowing out per second = Av Initial mass of water flowing out per second = Avd Rate of change of momentum = Adv2     Initial downward force on the flowing out water = Adv2 So equal amount of reaction acts upwards on the cylinder.  \ Initial upward reaction =\[Ad{{v}^{2}}\]  [As  \[v=\sqrt{2gh}\]] \[\therefore \] Initial decrease in weight \[=Ad\,(2gh)\] \[=2Adgh\]\[=2\times \left( \frac{1}{4} \right)\times 1\times 980\times 25=12.5\] gm-wt.


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