question_answer

A particle of mass m moving with horizontal speed 6 m/sec as shown in the figure. If \[m<M\], then for one dimensional elastic collision, the speed of lighter particle after collision will be

A) 2 m/sec in original direction

B) 2 m/sec opposite to the original direction

C) 4 m/sec opposite to the original direction

D) 4 m/sec in original direction

Correct Answer: A

Solution :

\[{{\nu }_{1}}=\left( \frac{{{m}_{1}}-{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}} \right){{u}_{1}}+\frac{2{{m}_{2}}{{u}_{2}}}{{{m}_{1}}+{{m}_{2}}}\] Substituting \[{{m}_{1}}=0,\,\,{{\nu }_{1}}=-{{u}_{1}}+2{{u}_{2}}\] \[\Rightarrow \,\,\,\,\,{{\nu }_{1}}= -6 + 2\left( 4 \right) = 2 m/s\] That is, the lighter particle will move in original direction with the speed of 2 m/s.