Laws Of Motion Question 349
Question: Two particles of equal mass are connected to a rope AB of negligible mass such that one is at end A and other dividing the length of rope in the ratio $ 1:2 $ from B. The rope is rotated about end B in a horizontal plane. Ratio of tensions in the smaller part to the other is (ignore effect of gravity)
Options:
A) $ 4:3~ $
B) $ 1:4 $
C) $ 1:2 $
D) $ 1:3 $
Show Answer
Answer:
Correct Answer: A
Solution:
[a]$ T _{1}=m{{\omega }^{2}}(3\ell ) $
and $ T _{2}-T _{1}=m{{\omega }^{2}}\ell $
or $ T _{2}=T _{1}+m{{\omega }^{2}}\ell =m{{\omega }^{2}}(3\ell )+m{{\omega }^{2}}\ell $
$ =4m{{\omega }^{2}}\ell $
$ \therefore \frac{T _{2}}{T _{1}}=\frac{4}{3} $
