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Inner core of a planet has mass M1 and radius r the outer layer has a mass M2 and extents up to radius 3 hours shown gravitational acceleration at the surface of the planet is as same as at the depth to our the ratio M2 ratio M1 is?
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Inner core of a planet has mass M1 and radius r the outer layer has a ...
Understanding the Gravitational Acceleration
The gravitational acceleration at the surface of a planet is determined by the total mass and radius of the planet. In this case, we have two distinct layers: an inner core and an outer layer.
Definitions and Variables
- Inner Core:
- Mass = M1
- Radius = r
- Outer Layer:
- Mass = M2
- Extends up to radius = 3r
Gravitational Acceleration Formula
The gravitational acceleration (g) at the surface of a spherical object is given by the formula:
g = GM/R^2
Where:
- G = Gravitational constant
- M = Total mass
- R = Radius
In our case, the total mass M of the planet can be expressed as:
M = M1 + M2
The radius at the surface is R = 3r.
Condition of Equal Gravitational Acceleration
It is given that the gravitational acceleration at the surface is the same as at the depth of the inner core. At depth d (where d = r), the formula for gravitational acceleration becomes:
g' = GM1/r^2
Setting the two gravitational accelerations equal gives us:
GM1/r^2 = G(M1 + M2)/(3r)^2
Deriving the Ratio M2/M1
After simplifying the above equation, we can express the ratio of the outer layer to the inner core:
M2/M1 = 9
This indicates that the mass of the outer layer is nine times the mass of the inner core.
Conclusion
Understanding the relationship between the two layers of the planet reveals that if the gravitational acceleration remains constant at the surface and at the depth of the inner core, the outer layer must contribute significantly more mass compared to the inner core. The derived ratio of M2 to M1 is 9:1.
The gravitational acceleration at the surface of a planet is determined by the total mass and radius of the planet. In this case, we have two distinct layers: an inner core and an outer layer.
Definitions and Variables
- Inner Core:
- Mass = M1
- Radius = r
- Outer Layer:
- Mass = M2
- Extends up to radius = 3r
Gravitational Acceleration Formula
The gravitational acceleration (g) at the surface of a spherical object is given by the formula:
g = GM/R^2
Where:
- G = Gravitational constant
- M = Total mass
- R = Radius
In our case, the total mass M of the planet can be expressed as:
M = M1 + M2
The radius at the surface is R = 3r.
Condition of Equal Gravitational Acceleration
It is given that the gravitational acceleration at the surface is the same as at the depth of the inner core. At depth d (where d = r), the formula for gravitational acceleration becomes:
g' = GM1/r^2
Setting the two gravitational accelerations equal gives us:
GM1/r^2 = G(M1 + M2)/(3r)^2
Deriving the Ratio M2/M1
After simplifying the above equation, we can express the ratio of the outer layer to the inner core:
M2/M1 = 9
This indicates that the mass of the outer layer is nine times the mass of the inner core.
Conclusion
Understanding the relationship between the two layers of the planet reveals that if the gravitational acceleration remains constant at the surface and at the depth of the inner core, the outer layer must contribute significantly more mass compared to the inner core. The derived ratio of M2 to M1 is 9:1.
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Inner core of a planet has mass M1 and radius r the outer layer has a mass M2 and extents up to radius 3 hours shown gravitational acceleration at the surface of the planet is as same as at the depth to our the ratio M2 ratio M1 is?
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Inner core of a planet has mass M1 and radius r the outer layer has a mass M2 and extents up to radius 3 hours shown gravitational acceleration at the surface of the planet is as same as at the depth to our the ratio M2 ratio M1 is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Inner core of a planet has mass M1 and radius r the outer layer has a mass M2 and extents up to radius 3 hours shown gravitational acceleration at the surface of the planet is as same as at the depth to our the ratio M2 ratio M1 is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Inner core of a planet has mass M1 and radius r the outer layer has a mass M2 and extents up to radius 3 hours shown gravitational acceleration at the surface of the planet is as same as at the depth to our the ratio M2 ratio M1 is?.
Inner core of a planet has mass M1 and radius r the outer layer has a mass M2 and extents up to radius 3 hours shown gravitational acceleration at the surface of the planet is as same as at the depth to our the ratio M2 ratio M1 is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Inner core of a planet has mass M1 and radius r the outer layer has a mass M2 and extents up to radius 3 hours shown gravitational acceleration at the surface of the planet is as same as at the depth to our the ratio M2 ratio M1 is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Inner core of a planet has mass M1 and radius r the outer layer has a mass M2 and extents up to radius 3 hours shown gravitational acceleration at the surface of the planet is as same as at the depth to our the ratio M2 ratio M1 is?.
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