Laws Of Motion Question 209
Question: Two trolleys of mass m and 3m are connected by a spring. They were compressed and released once, they move off in opposite direction and comes to rest after covering distances $ S _{1} $ and $ S _{2} $ respectively. Assuming the coefficient of friction to be uniform, the ratio of distances $ S _{1}:S _{2} $ is [EAMCET (Engg.) 1995]
Options:
A)1 : 9
B) 1 : 3
C) 3 : 1
D) 9 : 1
Show Answer
Answer:
Correct Answer: D
Solution:
When trolley are released then they posses same linear momentum but in opposite direction. Kinetic energy acquired by any trolley will dissipate against friction. $ \therefore $ $ \mu mgs=\frac{p^{2}}{2m} $
therefore $ s\propto \frac{1}{m^{2}} $ [As P and u are constants]therefore $ \frac{s _{1}}{s _{2}}={{( \frac{m _{2}}{m _{1}} )}^{2}}={{( \frac{3}{1} )}^{2}}=\frac{9}{1} $
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