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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\[{{m}_{1}}\]and\[{{m}_{2}}\] have equal momenta. Their kinetic energies are in the ratio of

    A)  \[\sqrt{{{m}_{1}}}:\sqrt{{{m}_{2}}}\]                     

    B)  \[{{m}_{1}}:{{m}_{2}}\]

    C)  \[{{m}_{2}}:{{m}_{1}}\]

    D)  \[{{m}_{1}}^{2}:{{m}_{2}}^{2}\]

    Correct Answer: C

    Solution :

       
    Body-1 Body-2
    Mass of the body\[({{m}_{1}})\] Mass of the body \[({{m}_{2}})\]
    \[='{{m}_{1}}'\,\,kg\] \[='{{m}_{2}}'\,\,kg\]
    We know, \[K.E.=\frac{{{P}^{2}}}{2m}\] Applying the above formula for two bodies we get, \[K.E{{.}_{1}}=\frac{{{P}^{2}}}{2\times {{m}_{1}}}\]                          ???..(1) \[K.E{{.}_{2}}=\frac{{{P}^{2}}}{2\times {{m}_{2}}}\]                          ???..(2) Dividing equation (1) by (2) we get, \[\frac{K.E{{.}_{1}}}{K.E{{.}_{2}}}=\frac{\frac{{{p}^{2}}}{2{{m}_{1}}}}{\frac{{{p}^{2}}}{2{{m}_{2}}}}=\frac{{{m}_{2}}}{{{m}_{1}}}\] \[\therefore \,\,K.E{{.}_{1}}:K.E{{.}_{2}}={{m}_{2}}:{{m}_{1}}\] 


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