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Three point Particle move in a circle with different but same speed . They start moving at t=0. The angular velocities of p q r are 5pi 3pi 2pi respectively . The time interval after which they all meet is?
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Three point Particle move in a circle with different but same speed . ...
Analysis:
To solve this problem, we need to find the time interval after which all three particles meet.
Step 1: Finding the angular speed of each particle:
Given that the angular velocities of particles p, q, and r are 5π, 3π, and 2π respectively. We can find the linear speed of each particle using the formula:
Linear speed = Angular speed x radius
Since all three particles are moving in a circle, the radius will be the same for all particles. Let's assume the radius is 'r'.
The linear speed of particle p = 5πr
The linear speed of particle q = 3πr
The linear speed of particle r = 2πr
Step 2: Finding the time taken by each particle to complete one revolution:
The time taken to complete one revolution is given by the formula:
Time taken = Circumference / Linear speed
Since the circumference of a circle is 2πr, the time taken by each particle to complete one revolution can be calculated as follows:
Time taken by particle p = (2πr) / (5πr) = 2/5 hours
Time taken by particle q = (2πr) / (3πr) = 2/3 hours
Time taken by particle r = (2πr) / (2πr) = 1 hour
Step 3: Finding the least common multiple (LCM) of the time taken by each particle:
To find the time interval after which all three particles meet, we need to find the LCM of the time taken by each particle.
The LCM of 2/5, 2/3, and 1 can be calculated as follows:
LCM(2/5, 2/3, 1) = LCM(6/15, 10/15, 15/15) = 15/15 = 1 hour
Conclusion:
Therefore, all three particles will meet after 1 hour.
To solve this problem, we need to find the time interval after which all three particles meet.
Step 1: Finding the angular speed of each particle:
Given that the angular velocities of particles p, q, and r are 5π, 3π, and 2π respectively. We can find the linear speed of each particle using the formula:
Linear speed = Angular speed x radius
Since all three particles are moving in a circle, the radius will be the same for all particles. Let's assume the radius is 'r'.
The linear speed of particle p = 5πr
The linear speed of particle q = 3πr
The linear speed of particle r = 2πr
Step 2: Finding the time taken by each particle to complete one revolution:
The time taken to complete one revolution is given by the formula:
Time taken = Circumference / Linear speed
Since the circumference of a circle is 2πr, the time taken by each particle to complete one revolution can be calculated as follows:
Time taken by particle p = (2πr) / (5πr) = 2/5 hours
Time taken by particle q = (2πr) / (3πr) = 2/3 hours
Time taken by particle r = (2πr) / (2πr) = 1 hour
Step 3: Finding the least common multiple (LCM) of the time taken by each particle:
To find the time interval after which all three particles meet, we need to find the LCM of the time taken by each particle.
The LCM of 2/5, 2/3, and 1 can be calculated as follows:
LCM(2/5, 2/3, 1) = LCM(6/15, 10/15, 15/15) = 15/15 = 1 hour
Conclusion:
Therefore, all three particles will meet after 1 hour.
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Three point Particle move in a circle with different but same speed . They start moving at t=0. The angular velocities of p q r are 5pi 3pi 2pi respectively . The time interval after which they all meet is?
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Three point Particle move in a circle with different but same speed . They start moving at t=0. The angular velocities of p q r are 5pi 3pi 2pi respectively . The time interval after which they all meet is? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Three point Particle move in a circle with different but same speed . They start moving at t=0. The angular velocities of p q r are 5pi 3pi 2pi respectively . The time interval after which they all meet is? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three point Particle move in a circle with different but same speed . They start moving at t=0. The angular velocities of p q r are 5pi 3pi 2pi respectively . The time interval after which they all meet is?.
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