Laws Of Motion Question 345

Question: A particle tied to a string describes a vertical circular motion of radius r continually. If it has a velocity $ \sqrt{3gr} $ at the highest point, then the ratio of the respective tensions in the string holding it at the highest and lowest points is

Options:

A) $ 4:3 $

B) $ 5:4 $

C) $ 1:4 $

D) $ 3:2 $

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Answer:

Correct Answer: C

Solution:

[c] Tension at the highest point

$ T _{top}=\frac{mv^{2}}{r}-mg=2mg( \therefore v _{top}=\sqrt{3gr} ) $

Tension at the lowest point

$ T _{bottom}=2mg+6mg=8mg $

$ \therefore \frac{T _{top}}{T _{bottom}}=\frac{2mg}{8mg}=\frac{1}{4}. $



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