Question

The centripetal acceleration of a body moving in circle of radius 100 m with time period 2s will be​

Answer 1

Given,

The radius of the circular path = 100 metres

Time period = 2 seconds

To find,

The centripetal acceleration of the moving body.

Solution,

First of all, we have to calculate the velocity of the moving body.

Now, the time period of an object which is in circular motion, is the time taken by that object to travel the distance equal to the circumference of that circular path.

Circumference of the circular path = 2 × π × 100

= 200π metres

The body can,

Travel in 2 seconds = 200π metres

Travel in 1 second = 200π/2 = 100π metres

The approximate velocity of the moving body = 200π m/s

So, the centripetal acceleration will be

= (velocity)²/radius

= (100π)²/100

= 10000π²/100

= 100×π²

= 100 × 22/7 × 22/7

= 48400/49

= 987.75 m/s²

Hence, the centripetal acceleration is 987.75 m/s².