Question

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 ?

1) mr : mr
2) m : m
3) r : r
4) 1 : 1

Answer 1

The ratio of the linear velocities of two particles of mass m moving in circles of the same radius r with equal time-periods is 1:1, which is the correct option for this physics question.

Step-by-step explanation:

If two particles of mass m are moving in a circle of radii r and their time-periods are the same, we can determine the ratio of their linear velocities. In circular motion, the linear velocity v is related to the radius r and the period T by the equation v = (2πr) / T, where 2πr is the circumference of the circle and T is the time taken to complete one revolution.

Since both particles have the same time-period, T, and the same radius, r, we substitute these equal values into the equation:

v1 = (2πr1) / T
v2 = (2πr2) / T

Given that r1 = r2, the linear velocities of both particles are the same:

v1 = v2

Therefore, the ratio of their linear velocities is 1 : 1.

The correct option for the question is the fourth option, 1 : 1.