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 $

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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} $



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