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JEE Main & Advanced Sample Paper JEE Main Sample Paper-13

  • question_answer
    A water barrel having water up to a depth d is placed on a table of height h. A small hole is made on the wall of the barrel at its bottom. If the stream of water coming out of the hole falls on the ground at a horizontal distance R from the barrel, then the value of d is

    A)  \[\frac{4h}{{{R}^{2}}}\]                                

    B)  \[4h{{R}^{2}}\]

    C)  \[\frac{{{R}^{2}}}{4h}\]                                

    D)  \[\frac{h}{4{{R}^{2}}}\]

    Correct Answer: C

    Solution :

     Velocity of efflux, \[{{E}^{f}}=-\frac{GMm}{2(2R+R)}\] Time taken for the range. \[[\because \,\,\text{height}\,=2R)\] Range = velocity \[={{E}_{f}}-{{E}_{i}}\] time \[\Rightarrow \] or      \[\Delta E=\frac{-GMm}{6R}+\frac{GMm}{R}=\frac{5}{6}\,\frac{GMm}{R}\] \[\Rightarrow \]               \[\Delta E=\frac{5}{6}\,mgR\]


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