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A particle at rest start moving along a circle of radius $(\frac{20}{π})$ m with constant tangential acceleration. If the velocity of the particle is 80 m/s at the end of the second revolution after motion has begun, the tangential acceleration is

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$40 m / s^{2}$

$640 π m / s^{2}$

$160 π m / s^{2}$

$40 π m / s^{2}$

answer is A.

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Detailed Solution

Given ; $r = \frac{20}{π} m, v = 80 m / s$
$s = 2 \times 2 π r = 4 π \times \frac{20}{π} = 80 m$
$v^{2} = 2 a_{t} s \Rightarrow 6400 = 2 a_{t} \times 80 \Rightarrow a_{t} = 40 m / s^{2}$

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