Question

A ball of mass m moves on circular paths of radius r₁ and r₂ with speed v₁ and v₂ respectively. If r₁ < r₂ then establish the relation between v₁ and v₂ while centripetal acceleration in both situations is same.

Answer 1

Centripetal acceleration, a_c = \(\frac {v_2}r\)

\(\because a_1 = a_2 \)

\(\therefore \frac{v_1^2}{r_1} = \frac{v_2^2}{r_2}\)

or \(\frac{v_1^2}{v_2^2} = \frac{r_1}{r_2}\)

or \(\frac{v_1}{v_2} = \sqrt{r_1} r_2 \quad .....(1)\)

∵ Given, r₁ < r₂

∴ Hence, v₁ < v₂