Question

Two bodies of masses 3kg and 5khn are moving at a uniform speed along a circular path of radius 5m and 3m respectively. If they take equal time to describe the circles completely, find the ratio of their angular velocities

Answer 1

Given,

Mass of one body, m1 = 3kg
Mass of second body, m2 = 5kg

Circular radius of first body, r1 = 5m
Circular radius of second body, r2 = 3m

Also, v1 = 2πr1/T [Both bodies have equal time to complete one circle]

And, v2 = 2πr2/T

Now,

Angular velocity of first body, ω1 = v1/r1 = 2πr1/T/r1 = 2π × 5/5T = 10π/5T
= 2π/T

Amgular velocity of second body, ω2 = v2/r2 = 2πr2/T/r2 = 2π × 3/3T
= 6π/3T = 2π/T

Now,

Ratio of angular velocities, ω1/ω2 = 2π/T/2π/T = 1:1

Answer 2

your answer is "1:1"

hope it will help you..