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A particle of mass M moves at a constant speed of v along the line y=d. Find the rate of change of the magnitude of the gravitational field at the origin when the particle is crossing the coordinates(d,d)?
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A particle of mass M moves at a constant speed of v along the line y=d...
Given:
- Mass of the particle (M)
- Constant speed of the particle (v)
- Particle moves along the line y=d
To find:
- Rate of change of the magnitude of the gravitational field at the origin when the particle is crossing the coordinates (d,d)
Approach:
1. We will first find the gravitational field due to the particle at the origin.
2. Then, we will differentiate the gravitational field with respect to time to find the rate of change.
Calculation:
1. Gravitational field due to the particle at the origin:
- The gravitational field (E) due to a particle at a distance r is given by the formula: E = G * (M / r^2), where G is the universal gravitational constant.
- In this case, the distance between the particle and the origin is always d, as the particle moves along the line y=d.
- Therefore, the gravitational field (E) at the origin is given by: E = G * (M / d^2).
2. Rate of change of the gravitational field at the origin:
- The rate of change of a quantity with respect to time is given by its derivative.
- Since the speed of the particle is constant, the time derivative of the gravitational field will be zero.
- Therefore, the rate of change of the magnitude of the gravitational field at the origin when the particle is crossing the coordinates (d,d) is zero.
Conclusion:
- The rate of change of the magnitude of the gravitational field at the origin when the particle is crossing the coordinates (d,d) is zero.
- Mass of the particle (M)
- Constant speed of the particle (v)
- Particle moves along the line y=d
To find:
- Rate of change of the magnitude of the gravitational field at the origin when the particle is crossing the coordinates (d,d)
Approach:
1. We will first find the gravitational field due to the particle at the origin.
2. Then, we will differentiate the gravitational field with respect to time to find the rate of change.
Calculation:
1. Gravitational field due to the particle at the origin:
- The gravitational field (E) due to a particle at a distance r is given by the formula: E = G * (M / r^2), where G is the universal gravitational constant.
- In this case, the distance between the particle and the origin is always d, as the particle moves along the line y=d.
- Therefore, the gravitational field (E) at the origin is given by: E = G * (M / d^2).
2. Rate of change of the gravitational field at the origin:
- The rate of change of a quantity with respect to time is given by its derivative.
- Since the speed of the particle is constant, the time derivative of the gravitational field will be zero.
- Therefore, the rate of change of the magnitude of the gravitational field at the origin when the particle is crossing the coordinates (d,d) is zero.
Conclusion:
- The rate of change of the magnitude of the gravitational field at the origin when the particle is crossing the coordinates (d,d) is zero.
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A particle of mass M moves at a constant speed of v along the line y=d. Find the rate of change of the magnitude of the gravitational field at the origin when the particle is crossing the coordinates(d,d)?
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A particle of mass M moves at a constant speed of v along the line y=d. Find the rate of change of the magnitude of the gravitational field at the origin when the particle is crossing the coordinates(d,d)? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A particle of mass M moves at a constant speed of v along the line y=d. Find the rate of change of the magnitude of the gravitational field at the origin when the particle is crossing the coordinates(d,d)? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle of mass M moves at a constant speed of v along the line y=d. Find the rate of change of the magnitude of the gravitational field at the origin when the particle is crossing the coordinates(d,d)?.
A particle of mass M moves at a constant speed of v along the line y=d. Find the rate of change of the magnitude of the gravitational field at the origin when the particle is crossing the coordinates(d,d)? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A particle of mass M moves at a constant speed of v along the line y=d. Find the rate of change of the magnitude of the gravitational field at the origin when the particle is crossing the coordinates(d,d)? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle of mass M moves at a constant speed of v along the line y=d. Find the rate of change of the magnitude of the gravitational field at the origin when the particle is crossing the coordinates(d,d)?.
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