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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2010

  • question_answer
        An open knife edge of mass M is dropped from a height h on a wooden floor. If the blade penetrates distance into the wood, the average resistance offered by the wood to the blade is

    A)  \[Mg\]                                

    B)  \[Mg\left( 1+\frac{h}{s} \right)\]

    C)  \[Mg\left( \frac{1-h}{s} \right)\]                             

    D)  \[Mg{{\left( \frac{1+h}{s} \right)}^{2}}\]

    Correct Answer: B

    Solution :

                    Let F be the resistive force of wooden plank. It will be acting opposite to the weight of body therefore, resultant force opposite to motion \[=F-Mg\] Velocity of fall\[=\sqrt{2gh}\] Work done\[=(F-Mg)s=\] kinetic energy                 \[=\frac{1}{2}M{{(\sqrt{2gh})}^{2}}\] or            \[F=\frac{Mgh}{s}+Mg\]                 \[=Mg\left( 1+\frac{h}{s} \right)\]


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