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9th Class Science Work and energy Question Bank Work Power and Energy IIT JEE Objective Problems

  • question_answer
    Two bodies of masses 1 m and 4 m have the same K.E. What is the ratio for their momenta.

    A)  2 : 1                                      

    B)  1 : 2

    C)  1 : 4                                      

    D)  4 : 1

    Correct Answer: B

    Solution :

     
    Body-1 Body-2
    Mass\[({{m}_{1}})='m'\,\,kg\] Mass \[({{m}_{2}})='4m'\,\,kg\]
    \[K.{{E}_{1}}=K.E.\] \[K.{{E}_{2}}=K.E.\]
                                    \[{{p}_{1}}:{{p}_{2}}=?\] We know that,\[K.E.=\frac{{{p}^{2}}}{2m}\](\[\because \]K.E is same for two bodies) Applying the above formula for two bodies, we get \[K.E{{.}_{1}}=\frac{p_{1}^{2}}{2{{m}_{1}}}\]                                      ??..(1) \[K.E{{.}_{2}}=\frac{p_{2}^{2}}{2\times 4{{m}_{2}}}=\frac{P_{2}^{2}}{9{{m}_{2}}}\]                          ??..(2) Given, K.E is same for two bodies therefore equation(1) = equation (2) Therefore, \[\frac{P_{1}^{2}}{2{{m}_{1}}}=\frac{P_{2}^{2}}{8{{m}_{2}}}\Rightarrow \frac{P_{1}^{2}}{P_{2}^{2}}=\frac{1}{4}\] \[\Rightarrow \frac{{{p}_{1}}}{{{p}_{2}}}=\frac{1}{2}\] \[\therefore \,\,{{P}_{1}}:{{P}_{2}}=1:2\]


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