Question

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

Answer 1

ac = v2/r

just took the test

Answer 2

The correct answer to the question is $a_{c} =\frac{v^2}{r}$

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.

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 $F_{c} =\frac{mv^2}{r}$.   [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 $a_{c} =\frac{v^2}{r}$.

Hence, the expression for centripetal acceleration is $\frac{v^2}{r}$