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A point starts from rest and moves along a circular path with a constant tangential acceleration. After one rotation, the ratio of its radial acceleration to its tangential acceleration will be equal to

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2 5. A point starts from rest and moves along a circular path with a constant tangential acceleration. After one rotation, the ratio of its radial acceleration to its tangential acceleration will be equal to (a) 1 (b) 2π (d) 4π

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Pratibha Jain

Grade 12

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Let the initial tangential acceleration of the point be “a”.

Let the radius of the circular path = R

Circumference of the circular path = 2πR

By using the third equation of motion: v2 = u2 + 2aS

We have initial velocity = u =0

acceleration = a ( dont get confused between the both a’s)

S = 2πR

from here we get v2 = 2 x a x 2πR = 4πRa

So velocity of the point after moving one complete rotation(2πR) = √4πRa

Now radial acceleration of the point after moving 1 complete rotation = v2/R = (√4πRa )2/R = 4πRa/R = 4πa

Since tangential acceleration was constant throughout the path from beginning so it is equal to a

Ratio = a / 4πa = 1/4π Answer