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Q.

A particle moves along a circle of radius $(\frac{20}{π}) m$ with constant tangential acceleration if the velocity of the particle $80 m/sec$ , at the end of second revolution after motion has begun the tangential acceleration is

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a

40 {m/sec}^{2}

b

640 π {m/sec}^{2}

c

1609 π {m/sec}^{2}

d

40 π {m/sec}^{2}

answer is A.

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Detailed Solution

r = \frac{20}{π}, v = 80 m/s

$θ = 4 π$

$ω = \frac{v}{r} = 4 π$

$ω^{2} = 2 α θ$

$α = 2 π$

$a_{t} = r α$

$= (\frac{20}{π}) (2 π)$

$a_{t} = 40 {m/s}^{2}$

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A particle moves along a circle of radius (20π)m with constant tangential acceleration if the velocity of the particle 80 m/sec , at the end of second revolution after motion has begun the tangential acceleration is