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A boy is running on a circular path with acceleration a if its velocity gets tripled, then find the ratio of acceleration after and before the change of velocity.

A boy is running on a circular path with acceleration a if its velocity gets tripled, then find the ratio of acceleration after and before the change of velocity. Correct Answer 9 : 1

CONCEPT:

  • Circular motion: It is a movement of an object along the circumference of a circle or rotation along a circular path.
    • It can be uniform, with the constant angular rate of rotation and constant speed, or non-uniform with a changing rate of rotation.
    • Some of the most common examples of circular motion include: 
    1. Man-made satellite that revolves around the earth
    2. A rotating ceiling fan, a moving car’s wheel
    3. The blades in a windmill, and gears in gas turbines.
    • ​The acceleration of a particle in a circular motion is always directed towards the center.
    • And the centripetal force acting towards center is given by:

Formula:

acceleration (a) = v2/r 

Centripetal force (Fc) = ma = mv2/r

CALCULATION:

Given that, v2 = 3v1, initially velocity v1 = 1 m/s

From the above discussion its clear that,

acceleration (a) = v2/r 

a1 = v12 / r    .....(i)

a2 = v22 / r = 9v12 / r    ...(ii)

Equating (i) and (ii) is

a1 = a2

v12 / r = 9v12 / r = 9 a1

The correct option is 9:1

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