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WB JEE Medical WB JEE Medical Solved Paper-2013

  • question_answer
    An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass 1 kg moves with a speed of \[12\,m{{s}^{-1}}\] and the second part of mass 2 kg moves with \[8\,m{{s}^{-1}}\] speed. If the third part flies off with \[4\,m{{s}^{-1}}\] speed, then its mass is

    A)  3 kg           

    B)  5 kg

    C)  7kg   

    D)  17kg

    Correct Answer: B

    Solution :

     We have \[{{p}_{1}}+{{p}_{2}}+{{p}_{3}}=0\]  \[[\because \,P=mv]\] \[\therefore \] \[1\times 12i+2\times 8j+{{p}_{3}}=0\] \[\Rightarrow \] \[12i+16j+{{p}_{3}}=0\] \[\Rightarrow \] \[{{p}_{3}}=-(12i+16j)\] \[\therefore \] \[{{p}_{3}}=\sqrt{{{(12)}^{2}}+{{(16)}^{2}}}\] \[=\sqrt{144+256}\] \[=20\,kg-m/s\] Now, \[{{p}_{3}}={{m}_{3}}{{v}_{3}}\] \[\Rightarrow \] \[{{m}_{3}}=\frac{{{p}_{3}}}{{{v}_{3}}}=\frac{20}{4}=5kg\]


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