question_answer

A body of mass 5 kg makes an elastic collision with another body at rest and continues to move in the original direction after collision with a velocity equal to \[\frac{1}{10}\] th of its original velocity. Then the mass of the second body is

A)  4.09 kg                

B)  0.5 kg

C)   5 kg                                     

D)  5.09 kg

Correct Answer: A

Solution :

 For elastic collision, \[e=1\] Given that, \[\text{Ist}\]body moves and \[\text{IInd}\]body is at rest After collision velocity of 5 kg mass becomes \[\frac{u}{10}.\] By law of conservation of momentum, \[{{m}_{1}}{{u}_{1}}+{{m}_{2}}{{u}_{2}}={{m}_{1}}{{u}_{1}}+{{m}_{2}}{{u}_{2}}\] \[\therefore \] \[5\times u+M\times 0=5\times \frac{u}{10}+M{{v}_{2}}\] or            \[5u-\frac{u}{2}=M{{v}_{2}}\] or            \[\frac{9u}{2}=M{{v}_{2}}\]                                         ?(i) Also .         \[{{v}_{1}}-{{v}_{2}}=-e({{u}_{1}}-{{u}_{2}})\] But e = 1 (e = coefficient of restitution) \[\therefore \]                  \[\frac{u}{10}-{{v}_{2}}=-(u)\] or                            \[\frac{u}{10}+u={{v}_{2}}\] or                            \[\frac{11u}{10}={{v}_{2}}\]                        ?(ii) Substituting the value of \[{{v}_{2}}\]in Eq. (i), we get                                                       \[\frac{9}{2}u=M\left( \frac{11u}{10} \right)\]                 or                            \[\frac{5\times 9}{11}=M\] or                            \[M=\frac{45}{11}=4.09\,kg\]