Question

Two cars of mass m₁ and m₂ are moving on circular path of radii r₁ and r₂ .Their speed is such that they complete circular path in same time t. Ratio of their centripetal acceleration is:

(a) m₁r₁ : m₂r₂

(b) m₁ : m₂

(c) r₁ : r₂ 

(d) 1 : 1

Answer 1

Correct option is : (c) r₁ : r₂ 

Since the time periods of cars are same, therefore their angular velocities will also be same.

∵ Centripetal acceleration a = rω²

^{\(\therefore\ \frac{a_1}{a_2} = \frac{r_1\omega^2}{r_2\omega^2} = \frac{r_1}{r_2\ }\ or\ \frac{a_1}{a_2} = \frac{r_1}{r_2}\)}

∴ Option (c) is correct.