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}} $



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