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NEET Sample Paper NEET Sample Test Paper-86

  • question_answer
    A diametrical tunnel is dug across the earth. A ball is dropped into the tunnel from one side. The velocity of the ball when it reaches the centre of the earth is (Given : gravitational potential at the centre of earth\[=-\frac{3}{2}\frac{GM}{R})\]

    A) \[\sqrt{R}\]                    

    B)        \[\sqrt{gR}\]

    C) \[\sqrt{2.5gR}\]  

    D)        \[\sqrt{7.1gR}\]

    Correct Answer: B

    Solution :

    [b] Loss in potential energy = Gainjn kinetic energy \[-\frac{GMm}{R}-\left( -\frac{3}{2}\frac{GMm}{R} \right)=\frac{1}{2}m{{v}^{2}}\] \[\Rightarrow \]\[\frac{GMm}{2R}=\frac{1}{2}m{{v}^{2}}\]\[\Rightarrow \]\[v=\sqrt{\frac{GM}{R}}=\sqrt{gR}\]


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