question_answer

Three identical spherical balls A, B and C are placed on a table as shown in the figure along a straight line. B and C are at rest initially. The ball A hits B head on with a speed of \[10\text{ }m{{s}^{-1}}.\] Then after all collisions (assumed to be elastic) A and B are brought to rest and C takes off with a velocity of

A) \[5m{{s}^{-1}}\]                                               

B) \[10m{{s}^{-1}}\]

C)  \[2.5m{{s}^{-1}}\]                                          

D)  \[7.5m{{s}^{-1}}\]

Correct Answer: B

Solution :

                 Here, \[{{\mu }_{1}}=10,{{m}_{1}}=m,{{m}_{2}}=m,{{u}_{2}}=0\] \[{{u}_{1}}=10\text{ }m/s\] \[{{v}_{2}}=\left[ \frac{{{m}_{2}}-{{m}_{1}}}{{{m}_{1}}+{{m}_{2}}} \right]{{u}_{2}}+\frac{2{{m}_{1}}{{u}_{1}}}{{{m}_{1}}+{{m}_{2}}}\] \[=\frac{2\times m\times 10}{2m}=10\,m/s\] Similarly, for B and C \[\Rightarrow \]               \[{{v}_{3}}=10\text{ }m/s\]