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A student whirls a stone in a horizontal circle of radius 3 m and at height 8 m above level ground. The string breaks and the stone flies off horizontally and strikes the ground after travelling a horizontal distance of 20 m. What is the magnitude of the centripetal acceleration of the stone while breaking off ?

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150 $m s^{- 2}$

140 $m s^{- 2}$

81.4 $m s^{- 2}$

163 $m s^{- 2}$

answer is C.

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Detailed Solution

$t = \sqrt{\frac{2 h}{g}} = \sqrt{\frac{2 \times 8}{9.8}} = 1.28 s$

$∵ v = \frac{20}{t} = 15.63 {ms}^{- 1}$

$∴ a = \frac{v^{2}}{R} = 81.4 {ms}^{- 2}$

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