Question

A car going around a curve of radius R at a speed V experiences a centripetal acceleration ac. What should be the radius of the path that leads to same centripetal acceleration while it travels at speed 2V

Answer 1

4R

Step-by-step explanation:

The centripetal acceleration a is given by a = v²/r where V = speed of object and r = radius of circle. Now, it is given that V = speed of car = V and radius of circle = R, so its centripetal acceleration a = V²/R.

Now, if the speed is doubled to V' = 2V with the same centripetal acceleration, we find the new radius of the curve R' from

a = V'²/R'

R' = V'²/a

R' = (2V)² ÷ V²/R

R' = 4V²R/V²

R' = 4R

So, the new radius is 4 times the initial radius.