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NEET AIPMT SOLVED PAPER MAINS 2012

  • question_answer
    A stone is dropped from a height h. It hits the ground with a certain momentum p. If the same stone is dropped from a height 100% more than the previous height, the momentum when it hits the ground will change by

    A)  68%                      

    B)  41%                      

    C)  200%                   

    D)  100%

    Correct Answer: B

    Solution :

    Velocity \[v=\sqrt{2gh}\]                                                ...(i) and momentum p = mv                ... (ii) From Eqs. (i) and (ii), we have \[p\propto \sqrt{h}\]                 Here                      \[\frac{{{p}_{2}}}{{{p}_{1}}}=\sqrt{\frac{{{h}_{2}}}{{{h}_{1}}}}\]                 \[\therefore \]                  \[\frac{{{p}_{2}}}{{{p}_{1}}}=\sqrt{\frac{2h}{h}}=\sqrt{2}\]                                                 \[{{p}_{2}}=1.414{{p}_{1}}\]                 % change \[=\frac{{{p}_{2}}-{{p}_{1}}}{{{p}_{1}}}\times 100=41%\]


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