A particle moves in a circular path with a radius of 10 m at a speed of 5 m/s. W

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Question: A particle moves in a circular path with a radius of 10 m at a speed of 5 m/s. What is the time period of the motion?

Options:

Correct Answer: 2π s

Solution:

Time period (T) = (2πr)/v = (2π * 10)/5 = 4π s.

A particle moves in a circular path with a radius of 10 m at a speed of 5 m/s. What is the time period of the motion?

A particle moves in a circular path with a radius of 10 m at a speed of 5 m/s. What is the time period of the motion?

Step 1: Identify the radius of the circular path. In this case, the radius (r) is 10 meters.
Step 2: Identify the speed of the particle. Here, the speed (v) is 5 meters per second.
Step 3: Use the formula for the time period (T) of circular motion, which is T = (2πr) / v.
Step 4: Substitute the values into the formula: T = (2π * 10) / 5.
Step 5: Calculate the numerator: 2π * 10 = 20π.
Step 6: Divide the result by the speed: T = 20π / 5.
Step 7: Simplify the division: T = 4π seconds.

Circular Motion – The motion of a particle along a circular path, where the time period is calculated using the radius and speed.
Time Period Calculation – The time taken for one complete revolution around the circular path, derived from the formula T = (2πr)/v.