Question

A body moving along a circular path of radius R with velocity v, has centripetal acceleration a. If its velocity is made equal to 2v. What will be the centripetal acceleration?

Options

• 4a

• 2a

• `"a"/4`

• `"a"/2`

Answer 1

4a

Explanation:

We know that centripetal acceleration is given by

a = `"V"^2/"R"`

For constant R

`"a" ∝ "V"^2` or `"a"_1/"a"_2 = "V"_1^2/"V"_2^2`

∴ `"a"_1/"a"_2 = "v"^2/(2"v")^2 = 1/4`

a₂ = 4a₁ or a₂ = 4a ....(∵ a₂ = a)