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Question

# A particle starting from rest moves with constant tangential acceleration on a circular path of radius 10π m. After 2.5 rotation the velocity of the particle is 50 m/s, its tangential acceleration is

A
25 m/s2
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B
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C
2500π2 m/s2
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D
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Solution

## The correct option is A 25 m/s2It is given that the particle strating from rest, its initial angular velocity ω0=0 and let say the final angular velocity is ω=vr=50π10=5π rad/s The angular displacement covered after 2.5 revolution is θ=2π×n=2π×2.5=5π rad By the equation of motion in circular kinematics we get, θ=ω2−ω202α,⇒α=25π210π=2.5π rad/s2 Now we know that the tangential acceleration aT=rα ⇒aT=10π×2.5π=25 m/s2 Hence option A is the correct answer

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