A particle moves in a circular path of radius 10 m with a constant speed of 5 m/

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

Options:

Correct Answer: 2π s

Solution:

Circumference = 2πr = 20π m. Period T = distance/speed = 20π m / 5 m/s = 4π s.

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

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

Step 1: Identify the radius of the circular path, which is given as 10 m.
Step 2: Use the formula for the circumference of a circle, which is Circumference = 2πr.
Step 3: Substitute the radius into the formula: Circumference = 2π(10 m) = 20π m.
Step 4: Identify the constant speed of the particle, which is given as 5 m/s.
Step 5: Use the formula for the period of motion, which is Period T = distance/speed.
Step 6: Substitute the values into the formula: T = (20π m) / (5 m/s).
Step 7: Simplify the calculation: T = 4π s.

Circular Motion – Understanding the relationship between radius, speed, and period in uniform circular motion.
Circumference Calculation – Calculating the circumference of a circle using the formula 2πr.
Period of Motion – Determining the period of motion using the formula T = distance/speed.