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 \[10\,m{{s}^{-1}}\]. Then after all collisions (assumed to be elastic) A and B are brought to rest and C takes off with a velocity of

A)  \[5\,m{{s}^{-1}}\]

B)  \[10\,m{{s}^{-1}}\]

C)  \[2.5\,m{{s}^{-1}}\]

D)  \[7.5\,m{{s}^{-1}}\]

Correct Answer: B

Solution :

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