Question

Which formula can be used to find the centripetal acceleration of an orbiting object?

Answer 1

ac = v2/r

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Answer 2

The correct answer to the question is
`a_(c) =(v^2)/(r)`

Here, v is the tangential velocity of the particle .

r is the radius of the orbit.

`a_(c)` is the centripetal acceleration of the body.

Step-by-step explanation:

When a body moves in a circular path, a centripetal force is needed to keep the body along its circular path.

Let us consider a body having mass m which is orbiting around any other object with a speed v .

Let r is the radius of the orbit.

Hence, the centripetal force needed to keep the object sticking to the orbit is calculated as -

Centripetal force
`F_(c) =(mv^2)/(r)`. [1]

From newton's second law of motion, we know that the net external force is the product of mass with the acceleration .

Mathematically F = ma . [2]

Here, the net force is the centripetal force and acceleration is the centripetal acceleration.

Hence, equation 2 can be written as
`F_(c) =\ ma_(c)` [3]

Comparing equations 1 and 2, we get
`a_(c) =(v^2)/(r)`.

Hence, the expression for centripetal acceleration is
`(v^2)/(r)`