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Question: Two particles of mass M and m are moving in a circle of radii R and r. If their time-periods are sam...

Two particles of mass M and m are moving in a circle of radii R and r. If their time-periods are same, what will be the ratio of their linear velocities

A

MR :mr

B

M : m

C

R : r

D

1 : 1

Answer

R : r

Explanation

Solution

v1v2=r1ω1r2ω2\frac{v_{1}}{v_{2}} = \frac{r_{1}\omega_{1}}{r_{2}\omega_{2}}. Time periods are equal i.e. ω1=ω2\omega_{1} = \omega_{2}

∴v1v2=r1r2=Rr\therefore\frac{v_{1}}{v_{2}} = \frac{r_{1}}{r_{2}} = \frac{R}{r}