If the radius of curvature of the path of two particles of same mass are in the ratio 3:4, then in order to have constant centripetal force, their velocities will be in the ratio of

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(4) √3:2. Idea: F=(mv²)/r with F and m fixed means v²∝ r, so v∝√r. (v₁)/(v₂)=√(r₁)/(r₂)=√3/4=(√3)/2. So the ratio is √3:2. The direction of the dependence is the quickest check: on a wider bend the same force will sustain a greater speed, so the larger radius must carry the larger v — which rules out the first three options at once.

If the radius of curvature of the path of two particles of same mass are in the ratio 3:4, then in order to have constant centripetal force, their velocities will be in the ratio of

Step-by-step solution

Why the other options are wrong