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An athlete throws a discus from rest to a final angular velocity of 15 rad $s^{- 1}$ in 0.270 s before releasing it. During this, discus moves a circular arc of radius 0.810 m. Acceleration of the centre of the discuss just before it is released is

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180 ${ms}^{- 2}$

45 ${ms}^{- 2}$

187 ${ms}^{- 2}$

192 ${ms}^{- 2}$

answer is C.

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Detailed Solution

$ω = ω_{o} + α_{t} or ω = 0 + αt$

or $α = \frac{ω}{t} = \frac{15}{0.270} rad s^{- 2}$ ;

$a_{t} = α r = \frac{15}{0.270} \times 0.81 m / s^{2} = 45 m / s^{2}; a_{n} = ω^{2} r = 15^{2} \times 0.81 m / s^{2} = 182.25 m / s^{2}; T o t a l a c c e l e r a t i o n = \sqrt{{a_{t}}^{2} + {a_{n}}^{2}} = 187 m / s^{2};$

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