Two particles A and B are moving in uniform circular motion in concentric circles of radii r_A and r_B with speed v_A and v_B respectively. Their time period of rotation is the same. The ratio of angular speed of A to that of B will be :

Question

Question

Answer 1

CONCEPT:

Angular velocity- Angular velocity is defined as the rates at which the object is rotated about an axis and it is written as;

----(1)

here, T is the time period respectively.

CALCULATION:

Given that the two particles A and B are moving in the circular motion in concentric circles r_A and r_B as shown in the figure below,

The angular velocity of particle A. Using equation (1) we have,

-----(2)

and the angular velocity of particle b we have,

-----(3)

Now, by dividing equation (2) by equation (3) we get

The time of rotation is the same, therefore

TA = TB = T

Hence, option 4) is the correct answer.