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  4. A ball of mass 0.6 kg attached to a light inextensible string rotates in a vertical circle of radius 0.75 m such that it has a speed of 5 text ms-1 when the string is horizontal. Tension in string when it h horizontal on other side is (g=10ms-2)

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Q. A ball of mass 0.6 kg attached to a light inextensible string rotates in a vertical circle of radius 0.75 m such that it has a speed of $ 5\text{ }m{{s}^{-1}} $ when the string is horizontal. Tension in string when it h horizontal on other side is $ (g=10m{{s}^{-}}2) $

EAMCETEAMCET 2007

Solution:

Tension in the string when it makes angle $ \theta $ with the vertical, $ T=\frac{m{{v}^{2}}}{r}+mg\cos \theta $ When the string is horizontal, $ \theta ={{90}^{o}} $ Here, m = 0.6 kg, r = 0.75 m, v = 5 m/ s Hence, $ T=\frac{m{{v}^{2}}}{r}+mg\times 0=\frac{m{{v}^{2}}}{r} $ $ \therefore $ $ T=\frac{0.6\times {{(5)}^{2}}}{0.75}=20\,N $