question_answer

A stone of mass 1 kg is tied to a string 4 m long and is rotated at constant speed of \[40\text{ }m{{s}^{-1}}\] in a vertical circle. The ratio of the tension at the top and the bottom is-

A) 11 : 12

B) 39 : 41

C) 41 : 39

D) 12 :11

Correct Answer: B

Solution :

AT lowest point applying NLM

At lowest point

\[{{T}_{1}}-mg=\frac{m{{v}^{2}}}{r}\]

\[{{T}_{bottom}}=\frac{m{{v}^{2}}}{r}+mg\]

At highest point

\[{{T}_{2}}+mg=\frac{m{{v}^{2}}}{r}\]

\[{{T}_{2}}=mg-\frac{m{{v}^{2}}}{r}\]

\[{{T}_{top}}=\frac{m{{v}^{2}}}{r}-mg\]

\[\frac{{{T}_{top}}}{{{T}_{Bottom}}}=\frac{\frac{{{v}^{2}}}{r}-g}{\frac{{{v}^{2}}}{r}+g}=\frac{39}{41}\]