Question

If the radii of circular paths of two particles of same masses are in the
ratio of 1:2, then to have a constant centripetal force their velocities
should be in the ratio of
(A) 1: V2
(B) V2:1
(C) 4:1
(D) 1:4​

Answer 1

Explanation:

Given: Radius of first particle (r1) = r and radius of second particle (r2) = 2r. When a particle is moving in a circular path, then the centripetal force,

F = (mv²/r) or F . r ∝ v² or r∝ v²

Now,

(r₁/r₂) = (v₁/v₂)²

=> (v₁/v₂) = √r₁/r₂

=> v₁ : v₂ = 1 : √2

Hope it helps!