Question

Two cars having masses m₁and m₂ move in circles of radii r₁ and r₂ respectively. If they complete the circle in equal time. What is the ratio of their speeds and centripetal accelerations? (Ans: r₁/r₂,r₁/r₂)

Answer 1

Final Answer : $\boxed {r_1 /r_2 , r_1/r_2}$

Steps:
1) Since, Time period is same for both the cars.
$v \propto circumference\:\:of \:circle \\ => v\propto r$
Therefore,
$\bold {v_1 /v_2 = r_1/r_2}$

2) Angular velocity is same in both the cases.
Therefore,
$a \propto r \\ =>\blue {a_1/a_2 = r_1/r_2}$

Hence, we got our desired result.