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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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:

G1 Physics · Accepted Answer

Given, m₁ = m₂ r₁/r₂ = 3 4 \frac{3}{4} 4 3 ​ Centripetal force, F = mv²/r For same centripetal force, m₁v₁²/r₁ = m₂v₂²/r₂ Since m₁ = m₂, v₁/v₂ = √(r₁/r₂) = √( 3 4 \frac{3}{4} 4 3 ​ ) = √3/2 Hence, v₁ : v₂ = √3 : 2