Question

A particle is moving in a vertical circle. The tensions in the string when passing through two positions at angle 30? and 60? from vertical (lowest position) are $ {{T}_{1}} $ and $ {{T}_{2}} $ respectively, then

• A. $ {{T}_{1}}={{T}_{2}} $
• B. $ {{T}_{2}}>{{T}_{1}} $
• C. $ {{T}_{1}}>{{T}_{2}} $
• D. tension in the string always remains the same

Answer 1

Answer: (C)

Tension in the string $ T=\frac{m{{v}^{2}}}{r}+mg\cos \theta $ For $ \theta ={{30}^{o}},{{T}_{1}}=\frac{m{{v}^{2}}}{r}+mg\cos {{30}^{o}} $ For $ \theta ={{60}^{o}},{{T}_{2}}=\frac{m{{v}^{2}}}{r}+mg\cos {{60}^{o}} $ $ \therefore $ $ {{T}_{1}}>{{T}_{2}}. $