Question: A particle moves in a circular path with a radius of 15 m and completes one revolution in 10 seconds. What is the linear speed of the particle?
Options:
1.5 m/s
3 m/s
6 m/s
9 m/s
Correct Answer: 3 m/s
Solution:
Linear speed (v) = 2πr/T = 2π(15 m)/10 s = 3 m/s.
A particle moves in a circular path with a radius of 15 m and completes one revo
Practice Questions
Q1
A particle moves in a circular path with a radius of 15 m and completes one revolution in 10 seconds. What is the linear speed of the particle?
1.5 m/s
3 m/s
6 m/s
9 m/s
Questions & Step-by-Step Solutions
A particle moves in a circular path with a radius of 15 m and completes one revolution in 10 seconds. What is the linear speed of the particle?
Step 1: Identify the radius of the circular path, which is given as 15 meters.
Step 2: Identify the time taken to complete one full revolution, which is given as 10 seconds.
Step 3: Use the formula for linear speed, which is v = 2πr/T.
Step 4: Substitute the values into the formula: v = 2π(15 m)/10 s.
Step 5: Calculate the circumference of the circle: 2π(15 m) = 30π m.
Step 6: Divide the circumference by the time: 30π m / 10 s = 3π m/s.
Step 7: Approximate π as 3.14 to find the numerical value: 3 * 3.14 = 9.42 m/s.
Step 8: Conclude that the linear speed of the particle is approximately 9.42 m/s.
Circular Motion – The motion of a particle along a circular path, where linear speed can be calculated using the formula v = 2πr/T.
Linear Speed – The distance traveled per unit of time along the circular path, calculated as the circumference of the circle divided by the period.
Period of Revolution – The time taken to complete one full revolution around the circular path.
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