JEE Main · 2024 · 29 Jan 2024 · Shift 1 · Laws of Motion

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:

(A) $3 : 2$ ✓ Correct
(B) $1 : 3$
(C) $3 : 1$
(D) $2 : 3$

Answer: (A)

Solution

Centripetal force

F = \frac{m v ^{2}}{r}

is the same for both particles (same mass

m

\frac{v _{1}^{2}}{r _{1}} = \frac{v _{2}^{2}}{r _{2}} ⟹ \frac{v _{1}^{2}}{v _{2}^{2}} = \frac{r _{1}}{r _{2}} = \frac{3}{4} ⟹ \frac{v _{1}}{v _{2}} = \frac{3}{2}

Key confirmed: A.

JEE Main · 2024 · 29 Jan 2024 · Shift 1 · Single correct option

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