2. Questions Bank
  3. 9th Class
  4. Science
  5. Work and energy

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

  • question_answer
    The bodies of masses 2m and m have their kinetic energies in the ratio 8:1. Then the ratio of their momenta is

    A)  1 : 1       

    B)  2 : 1

    C)  4 : 1                                      

    D)  8 : 1

    Correct Answer: A

    Solution :

     
    Body-1 Body -2
    Mass\[({{m}_{1}})='2m'\,\,kg\] Mas \[({{m}_{2}})='m'\,\,kg\]
    \[K.{{E}_{1}}=8J\] \[K.{{E}_{2}}=1J\]
    \[{{p}_{1}}:{{p}_{2}}=1\,J\] We know, \[K.E.=\frac{{{p}^{2}}}{2m}\] Applying the above formula for two bodies we get, \[\Rightarrow K.E{{.}_{1}}=\frac{p_{1}^{2}}{2\times 2m}\Rightarrow K.E{{.}_{2}}=\frac{p_{2}^{2}}{2\times m}\] \[\Rightarrow 8=\frac{p_{1}^{2}}{4m}\Rightarrow 1=\frac{p_{2}^{2}}{2m}\] \[\Rightarrow p_{1}^{2}=32m\]                 ......(1)  \[\Rightarrow p_{2}^{2}=2m\]                   .......(2) Dividing equation (1) by (2) we get, \[\frac{p_{1}^{2}}{p_{1}^{2}}=\frac{32m}{2m}=\frac{16}{1}\Rightarrow \frac{{{P}_{1}}}{{{P}_{2}}}=\frac{4}{1}\] \[\therefore \,\,{{p}_{1}}:{{p}_{1}}=4:1\]             


You need to login to perform this action.
You will be redirected in 3 sec spinner