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  4. A mass attached to one end of a string crosses topmost point on a vertical circle with critical speed. Its centripetal acceleration when string becomes horizontal will be ( g= gravitational acceleration)

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Q. A mass attached to one end of a string crosses topmost point on a vertical circle with critical speed. Its centripetal acceleration when string becomes horizontal will be ( $g=$ gravitational acceleration)

NTA AbhyasNTA Abhyas 2020Laws of Motion

Solution:

Critical velocity at top most point $v = \sqrt{r g}$
$\therefore $ Velocity when string become horizontal
$v ' = \sqrt{\upsilon^{2} + 2 g r}$
$= \sqrt{3 g r}$
Centripetal acceleration $= \frac{\upsilon^{2}}{r} = \frac{3 r g}{r} = 3 g$