Laws Of Motion Question 425
Question: A spring is compressed between blocks of masses $ m _{1} $ and $ m _{2} $ placed on a smooth horizontal surface . When the blocks are release, they have initial velocity of $ v _{1} $ and $ v _{2} $ in the direction shown. The blocks travel distances $ x _{1} $ and $ x _{2} $ before coming to rest. The ratio of $ \frac{x _{1}}{x _{2}} $ is
Options:
A) $ \frac{m _{1}}{m _{2}} $
B) $ \sqrt{\frac{m _{1}}{m _{2}}} $
C) $ \frac{m _{2}}{m _{1}} $
D) $ \sqrt{\frac{m _{2}}{m _{1}}} $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] From linear momentum conservation, $ m _{1}v _{1}=m _{2}v _{2} $ .
As they move spring exerts equal and opposite forces on $ m _{1} $ and $ m _{2} $ .
$ \Rightarrow $ $ m _{1}\frac{dx _{1}}{dt}=m _{2}\frac{dx _{2}}{dt} $
$ \Rightarrow $ $ m _{1}\int{dx _{1}=m _{2}\int{dx _{2}}} $
$ \Rightarrow $ $ m _{1}x _{1}=m _{2}x _{2} $
$ \Rightarrow $ $ \frac{x _{1}}{x _{2}}=\frac{m _{2}}{m _{1}} $
