NEET Sample Paper NEET Sample Test Paper-39

  • question_answer A ball is thrown vertically downwards from a height of 20 m with an initial velocity\[v_{0}^{2}.\]It collides with the ground, loses 50 percent of its energy in collision and rebounds to the same height. The initial velocity \[{{v}_{0}}\]is: (Take\[g=10\,m{{s}^{-2}}\])

    A) \[~10\,m{{s}^{-1}}\]      

    B) \[~14\,m{{s}^{-1}}\]

    C) \[~20\,m{{s}^{-1}}\]      

    D) \[~28\,m{{s}^{-1}}\]

    Correct Answer: C

    Solution :

     Let ball rebound with speed v, so \[v=\sqrt{2gh}=\sqrt{2\times 10\times 20}=20\,m/s\] Energy just after rebound \[E=\frac{1}{2}\times m\times {{v}^{2}}=200\,m\] 50% energy loses in collision means just before collision energy is 400 m By using energy conservation, \[\frac{1}{2}mv_{0}^{2}+mgh=400\,m\] \[\Rightarrow \]\[\frac{1}{2}mv_{0}^{2}+m\times 10\times 20=400\Rightarrow {{v}_{0}}=20\,m/s\]

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