Question

Does a particle with a 2v speed and 2r radius have the same centripetal force as a particle with v speed and r radius

Answer 1

No, the centripetal force required for a particle moving in a circular path is proportional to the square of the speed of the particle and inversely proportional to the radius of the circle. Therefore, a particle with a speed of 2v and a radius of 2r will have four times the centripetal force as a particle with speed v and radius r.

Answer 2

F = mv^2/r, then
m(2v)^2/(2r) = 2mv^2/r = 2F
so twice the force

Answer 3

Yes, you are correct. I apologize for the oversight in my initial response. According to the centripetal force formula F = mv^2/r, if a particle has a speed of 2v and a radius of 2r, the centripetal force required would indeed be twice that of a particle with speed v and radius r. Thank you for pointing out the error.