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A particle is moving in a plane with a constant radial velocity 5 m/sec and constant angular velocity of 3 rad/sec. When the particle is at a distance r = 4 m from the origin, the magnitude of the instantaneous velocity of the particle in m/sec is
Correct answer is '13'. Can you explain this answer?
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Instantaneous Velocity in Polar Coordinates
The problem describes the motion of a particle in a plane using polar coordinates. The particle has a constant radial velocity of 5 m/sec and a constant angular velocity of 3 rad/sec. We need to find the magnitude of the instantaneous velocity when the particle is at a distance r = 4 m from the origin.
1. Understanding the Problem
We are given the following information:
- Radial velocity (v_r) = 5 m/sec
- Angular velocity (ω) = 3 rad/sec
- Distance from the origin (r) = 4 m
We need to find the magnitude of the instantaneous velocity (v) of the particle.
2. Deriving the Instantaneous Velocity
The velocity of a particle in polar coordinates consists of two components: the radial velocity and the tangential velocity. The instantaneous velocity (v) can be determined using the following equation:
v = √(v_r² + (rω)²)
3. Substituting Values
Let's substitute the given values into the equation:
v = √(5² + (4 * 3)²)
v = √(25 + 144)
v = √169
v = 13 m/sec
4. Conclusion
The magnitude of the instantaneous velocity of the particle at a distance r = 4 m from the origin is 13 m/sec.
Therefore, the correct answer is 13.
The problem describes the motion of a particle in a plane using polar coordinates. The particle has a constant radial velocity of 5 m/sec and a constant angular velocity of 3 rad/sec. We need to find the magnitude of the instantaneous velocity when the particle is at a distance r = 4 m from the origin.
1. Understanding the Problem
We are given the following information:
- Radial velocity (v_r) = 5 m/sec
- Angular velocity (ω) = 3 rad/sec
- Distance from the origin (r) = 4 m
We need to find the magnitude of the instantaneous velocity (v) of the particle.
2. Deriving the Instantaneous Velocity
The velocity of a particle in polar coordinates consists of two components: the radial velocity and the tangential velocity. The instantaneous velocity (v) can be determined using the following equation:
v = √(v_r² + (rω)²)
3. Substituting Values
Let's substitute the given values into the equation:
v = √(5² + (4 * 3)²)
v = √(25 + 144)
v = √169
v = 13 m/sec
4. Conclusion
The magnitude of the instantaneous velocity of the particle at a distance r = 4 m from the origin is 13 m/sec.
Therefore, the correct answer is 13.
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A particle is moving in a plane with a constant radial velocity 5 m/sec and constant angular velocity of 3 rad/sec. When the particle is at a distance r = 4 m from the origin, the magnitude of the instantaneous velocity of the particle in m/sec isCorrect answer is '13'. Can you explain this answer?
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A particle is moving in a plane with a constant radial velocity 5 m/sec and constant angular velocity of 3 rad/sec. When the particle is at a distance r = 4 m from the origin, the magnitude of the instantaneous velocity of the particle in m/sec isCorrect answer is '13'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about A particle is moving in a plane with a constant radial velocity 5 m/sec and constant angular velocity of 3 rad/sec. When the particle is at a distance r = 4 m from the origin, the magnitude of the instantaneous velocity of the particle in m/sec isCorrect answer is '13'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle is moving in a plane with a constant radial velocity 5 m/sec and constant angular velocity of 3 rad/sec. When the particle is at a distance r = 4 m from the origin, the magnitude of the instantaneous velocity of the particle in m/sec isCorrect answer is '13'. Can you explain this answer?.
A particle is moving in a plane with a constant radial velocity 5 m/sec and constant angular velocity of 3 rad/sec. When the particle is at a distance r = 4 m from the origin, the magnitude of the instantaneous velocity of the particle in m/sec isCorrect answer is '13'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about A particle is moving in a plane with a constant radial velocity 5 m/sec and constant angular velocity of 3 rad/sec. When the particle is at a distance r = 4 m from the origin, the magnitude of the instantaneous velocity of the particle in m/sec isCorrect answer is '13'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle is moving in a plane with a constant radial velocity 5 m/sec and constant angular velocity of 3 rad/sec. When the particle is at a distance r = 4 m from the origin, the magnitude of the instantaneous velocity of the particle in m/sec isCorrect answer is '13'. Can you explain this answer?.
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