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 $
Show Answer
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}. $
