Question

A car is making a turn at speed v. The radius of the
turn is r and the centripetal force on the car is F.
If the car rounds the same curve at speed 2v, the
required centripetal force is​

Answer 1

Given:

A car is making a turn at speed v. The radius of the turn is r and the centripetal force on the car is F.

To find:

Centripetal force when velocity becomes 2v?

Calculation:

• Centripetal force is a radially inwards force experienced by objects in circular trajectory.

Initial centripetal force is :

$F = \dfrac{m {v}^{2} }{r}$

• New velocity is 2v.

$F_{2} = \dfrac{m {(2v)}^{2} }{r}$

$\implies F_{2} = 4 \times \dfrac{m {v}^{2} }{r}$

$\implies F_{2} = 4 \times F$

So, the new centripetal force is 4F (i.e. 4 times the initial centripetal force).