A) \[{{m}_{1}}{{u}_{1}}+{{m}_{2}}{{u}_{2}}={{m}_{1}}v+{{m}_{2}}v\]
B) \[{{m}_{2}}{{u}_{1}}-{{m}_{1}}{{u}_{2}}=({{m}_{1}}+{{m}_{2}})v\]
C) \[{{m}_{1}}{{u}_{1}}-{{m}_{2}}{{u}_{2}}=({{m}_{1}}-{{m}_{2}})v\]
D) \[v=\frac{{{m}_{1}}{{u}_{1}}-{{m}_{2}}{{u}_{2}}}{{{m}_{1}}+{{m}_{2}}}\]
Correct Answer: D
Solution :
Since initially, the two bodies are moving in opposite direction, if velocity of one body is \[{{u}_{1}}\] then velocity of the other body is \[-{{u}_{2}}.\] Negative sign indicates that it is moving in opposite direction. so, \[{{m}_{1}}{{u}_{1}}+{{m}_{2}}{{u}_{2}}={{m}_{1}}v+{{m}_{2}}v=({{m}_{1}}+{{m}_{2}})v\] \[\Rightarrow V=\frac{{{m}_{1}}{{u}_{1}}+{{m}_{2}}{{u}_{2}}}{{{m}_{1}}+{{m}_{2}}}\]
You need to login to perform this action.
You will be redirected in
3 sec
