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A particle of mass M is revolving along a circle of radius R and another particle of mass M is revolving in a circle of radius r. if time periods of both particles are same then the ratio of the angular velocities is?
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A particle of mass M is revolving along a circle of radius R and anoth...
Introduction:
We are given two particles of equal mass M, revolving in circles of radii R and r respectively. The time periods of both particles are the same. We need to find the ratio of their angular velocities.
Explanation:
The angular velocity of a particle is defined as the rate of change of its angle with respect to time. It is denoted by the symbol ω.
The formula for angular velocity is:
ω = Δθ / Δt
Where:
ω is the angular velocity,
Δθ is the change in angle, and
Δt is the change in time.
Relation between angular velocity and time period:
The time period (T) of a particle is the time taken to complete one full revolution. It is the reciprocal of the frequency (f) of the particle's motion.
The formula for time period is:
T = 1 / f
The frequency (f) is the number of complete revolutions made by the particle in one second.
Since the time periods of both particles are the same, we can write:
T1 = T2
From the formula for time period, we know that:
T = 2π / ω
Therefore, we have:
2π / ω1 = 2π / ω2
Cancelling out the common terms, we get:
ω1 = ω2
Conclusion:
The ratio of the angular velocities of the two particles is 1:1, which means they have the same angular velocity. The mass and radius of the particles do not affect their angular velocities as long as their time periods are the same.
We are given two particles of equal mass M, revolving in circles of radii R and r respectively. The time periods of both particles are the same. We need to find the ratio of their angular velocities.
Explanation:
The angular velocity of a particle is defined as the rate of change of its angle with respect to time. It is denoted by the symbol ω.
The formula for angular velocity is:
ω = Δθ / Δt
Where:
ω is the angular velocity,
Δθ is the change in angle, and
Δt is the change in time.
Relation between angular velocity and time period:
The time period (T) of a particle is the time taken to complete one full revolution. It is the reciprocal of the frequency (f) of the particle's motion.
The formula for time period is:
T = 1 / f
The frequency (f) is the number of complete revolutions made by the particle in one second.
Since the time periods of both particles are the same, we can write:
T1 = T2
From the formula for time period, we know that:
T = 2π / ω
Therefore, we have:
2π / ω1 = 2π / ω2
Cancelling out the common terms, we get:
ω1 = ω2
Conclusion:
The ratio of the angular velocities of the two particles is 1:1, which means they have the same angular velocity. The mass and radius of the particles do not affect their angular velocities as long as their time periods are the same.
Community Answer
A particle of mass M is revolving along a circle of radius R and anoth...
1:1
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A particle of mass M is revolving along a circle of radius R and another particle of mass M is revolving in a circle of radius r. if time periods of both particles are same then the ratio of the angular velocities is?
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A particle of mass M is revolving along a circle of radius R and another particle of mass M is revolving in a circle of radius r. if time periods of both particles are same then the ratio of the angular velocities is? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A particle of mass M is revolving along a circle of radius R and another particle of mass M is revolving in a circle of radius r. if time periods of both particles are same then the ratio of the angular velocities is? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle of mass M is revolving along a circle of radius R and another particle of mass M is revolving in a circle of radius r. if time periods of both particles are same then the ratio of the angular velocities is?.
A particle of mass M is revolving along a circle of radius R and another particle of mass M is revolving in a circle of radius r. if time periods of both particles are same then the ratio of the angular velocities is? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A particle of mass M is revolving along a circle of radius R and another particle of mass M is revolving in a circle of radius r. if time periods of both particles are same then the ratio of the angular velocities is? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle of mass M is revolving along a circle of radius R and another particle of mass M is revolving in a circle of radius r. if time periods of both particles are same then the ratio of the angular velocities is?.
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