Two objects ① and ② are moving along two different circular paths of radii 10 m and 20 m respectively. If the ratio of their speeds ( V₁ : V₂) = 2:1, then the ratio of their time periods (T₁ : T₂) [ Use numerals to write your answer] *

The ratio of the time period of object 1 to the time period of object 2 is . (T₁ : T₂) = 1 : 4

Explanation:

Let suppose that both objects are moving along the circular paths at constant speed, such that period of rotation of each object is represented by the following formula:

Where:

- Angular speed, measured in radians per second.

- Period, measured in seconds.

The period is now cleared:

Angular speed () and linear speed () are related to each other by this formula:

Where is the radius of rotation, measured in meters.

The angular speed can be replaced and the resultant expression is obtained:

Which means that time period is directly proportional to linear speed and directly proportional to radius of rotation. Then, the following relationship is constructed and described below:

Where:

, - Time periods of objects 1 and 2, measured in seconds.

, - Linear speed of objects 1 and 2, measured in meters per second.

, - Radius of rotation of objects 1 and 2, measured in meters.

If , and , the ratio of time periods is:

The ratio of the time period of object 1 to the time period of object 2 is .

answer: 31, 5556. 952 seconds