A stone of mass 5 kg is tied to a string of length 10m is whirled round in a horizontal circle. What is the maximum speed with which the stone can be whirled around if the string can withstand a maximum tension of 200 N?

10 m s^{- 1}

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15 m s^{- 1}

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20 m s^{- 1}

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25 m s^{- 1}

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Solution

The correct option is C $20 m s^{- 1}$
Mass of the stone, $m = 5 k g$
Radius of the circle, $r = 10 m$
Maximum tension in the string, $T_{m a x} = 200 N$

Let $v_{m a x}$ be the maximum speed by which stone can be whirled

$⟹ T_{m a x} = \frac{m v_{m a x}^{2}}{r}$

$⟹ v_{m a x} = \sqrt{\frac{r T_{m a x}}{m}}$

$⟹ v_{m a x} = \sqrt{\frac{10 \times 200}{5}} = \sqrt{400} = 20 m / s$

So, option $(C)$ is correct.

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A stone of mass 5 kg is tied to a string of length 10m is whirled round in a horizontal circle. What is the maximum speed with which the stone can be whirled around if the string can withstand a maximum tension of 200 N?

The correct option is C 20ms−1Mass of the stone, m=5 kgRadius of the circle, r=10 mMaximum tension in the string, Tmax=200 NLet vmax be the maximum speed by which stone can be whirled ⟹Tmax=mv2maxr⟹vmax=√rTmaxm⟹vmax=√10×2005=√400=20 m/sSo, option (C) is correct.