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Two masses m1 and m2 are separated by distance r. Calculate gravitational potential at the point where gravitational field intensity (I)= 0.?
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Two masses m1 and m2 are separated by distance r. Calculate gravitatio...
Understanding Gravitational Potential and Field Intensity
Gravitational potential (V) and gravitational field intensity (I) are fundamental concepts in gravitation. The gravitational field intensity is defined as the force experienced by a unit mass at a point in a gravitational field.
Gravitational Field Intensity (I)
- The gravitational field intensity due to mass m1 at a distance r1 is given by:
I1 = G * m1 / r1²
- The gravitational field intensity due to mass m2 at a distance r2 is given by:
I2 = G * m2 / r2²
- At a point where the gravitational field intensity is zero, the magnitudes of I1 and I2 must be equal:
I1 = I2
Finding the Point of Zero Gravitational Field Intensity
- Let the distance from m1 to the point be r1 and from m2 to the point be r2. Given that r = r1 + r2, we can express r2 as:
r2 = r - r1
- Setting the equations equal:
G * m1 / r1² = G * m2 / (r - r1)²
- Simplifying gives the condition to find r1, and subsequently r2.
Calculating Gravitational Potential (V)
- The gravitational potential at the point of zero intensity is the sum of potentials due to both masses:
V = - (G * m1 / r1) - (G * m2 / r2)
- Substitute r2 with (r - r1) to compute V explicitly:
V = - (G * m1 / r1) - (G * m2 / (r - r1))
Conclusion
- The gravitational potential at the point where gravitational field intensity is zero can be calculated using the distances from both masses and their respective magnitudes.
Gravitational potential (V) and gravitational field intensity (I) are fundamental concepts in gravitation. The gravitational field intensity is defined as the force experienced by a unit mass at a point in a gravitational field.
Gravitational Field Intensity (I)
- The gravitational field intensity due to mass m1 at a distance r1 is given by:
I1 = G * m1 / r1²
- The gravitational field intensity due to mass m2 at a distance r2 is given by:
I2 = G * m2 / r2²
- At a point where the gravitational field intensity is zero, the magnitudes of I1 and I2 must be equal:
I1 = I2
Finding the Point of Zero Gravitational Field Intensity
- Let the distance from m1 to the point be r1 and from m2 to the point be r2. Given that r = r1 + r2, we can express r2 as:
r2 = r - r1
- Setting the equations equal:
G * m1 / r1² = G * m2 / (r - r1)²
- Simplifying gives the condition to find r1, and subsequently r2.
Calculating Gravitational Potential (V)
- The gravitational potential at the point of zero intensity is the sum of potentials due to both masses:
V = - (G * m1 / r1) - (G * m2 / r2)
- Substitute r2 with (r - r1) to compute V explicitly:
V = - (G * m1 / r1) - (G * m2 / (r - r1))
Conclusion
- The gravitational potential at the point where gravitational field intensity is zero can be calculated using the distances from both masses and their respective magnitudes.
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Two masses m1 and m2 are separated by distance r. Calculate gravitational potential at the point where gravitational field intensity (I)= 0.?
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Two masses m1 and m2 are separated by distance r. Calculate gravitational potential at the point where gravitational field intensity (I)= 0.? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two masses m1 and m2 are separated by distance r. Calculate gravitational potential at the point where gravitational field intensity (I)= 0.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two masses m1 and m2 are separated by distance r. Calculate gravitational potential at the point where gravitational field intensity (I)= 0.?.
Two masses m1 and m2 are separated by distance r. Calculate gravitational potential at the point where gravitational field intensity (I)= 0.? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two masses m1 and m2 are separated by distance r. Calculate gravitational potential at the point where gravitational field intensity (I)= 0.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two masses m1 and m2 are separated by distance r. Calculate gravitational potential at the point where gravitational field intensity (I)= 0.?.
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