question_answer

Two solid rubber balls A and B having masses 200 and 400 gm respectively are moving in opposite directions with velocity of A equal to 0.3 m/s. After collision the two balls come to rest, then the velocity of B is

A) 0.15 m/sec                    

B) 1.5 m/sec

C) - 0.15 m/sec                  

D) None of the above

Correct Answer: C

Solution :

Initial linear momentum of system         \[=\,\,\,{{m}_{A}}{{\vec{u}}_{A}}+{{m}_{B}}{{\vec{u}}_{B}}\] \[=0.2 \times  0.3 + 0.4 \times \,\,{{\nu }_{B}}\] Finally both balls come to rest             \[\therefore \] Final linear momentum = 0          By the law of conservation of linear momentum \[0.2 \times  0.3 + 0.4 \times \,\,{{\nu }_{B}}=0\] \[\therefore \,\,\,\,\,\,\,\,\,{{\nu }_{B}}=-\frac{0.2\times 0.3}{0.4}=-\,0.15\,\,m/s\]