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Suppose there are two planets, 1 and 2, having the same density but their radii are R1 and R2 respectively, where R1>R2. The accelerations due to gravity on the surface of this planet are related as
- a)g1 > g2
- b)g1 < g2
- c)g1 = g2
- d)Can’t say anything
Correct answer is option 'A'. Can you explain this answer?
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Suppose there are two planets, 1 and 2, having the same density but th...
Acceleration due to gravity 
As R1 > R2
⇒ g1 > g2
Most Upvoted Answer
Suppose there are two planets, 1 and 2, having the same density but th...
Understanding Gravity on Different Planets
The gravitational acceleration on the surface of a planet is determined by its mass and radius. Here's how we can analyze the situation for planets 1 and 2.
Formula for Gravitational Acceleration
The formula for gravitational acceleration (g) at the surface of a planet is given by:
g = G * (M / R^2)
Where:
- G is the gravitational constant.
- M is the mass of the planet.
- R is the radius of the planet.
Mass Calculation
Since both planets have the same density (ρ), we can express their masses as follows:
M1 = ρ * (4/3) * π * R1^3
M2 = ρ * (4/3) * π * R2^3
Comparing Gravitational Accelerations
Now we can substitute the expressions for mass into the gravity formula:
g1 = G * (ρ * (4/3) * π * R1^3) / R1^2
g2 = G * (ρ * (4/3) * π * R2^3) / R2^2
This simplifies to:
g1 = G * (ρ * (4/3) * π * R1)
g2 = G * (ρ * (4/3) * π * R2)
Now, since R1 > R2, it follows that:
g1 = (4/3) * π * G * ρ * R1
g2 = (4/3) * π * G * ρ * R2
Since R1 is greater than R2, we conclude that:
g1 > g2
Conclusion
Therefore, the correct answer is:
g1 > g2 (Option A)
This indicates that the gravitational acceleration on the surface of Planet 1 is greater than that on Planet 2, due to its larger radius while maintaining the same density.
The gravitational acceleration on the surface of a planet is determined by its mass and radius. Here's how we can analyze the situation for planets 1 and 2.
Formula for Gravitational Acceleration
The formula for gravitational acceleration (g) at the surface of a planet is given by:
g = G * (M / R^2)
Where:
- G is the gravitational constant.
- M is the mass of the planet.
- R is the radius of the planet.
Mass Calculation
Since both planets have the same density (ρ), we can express their masses as follows:
M1 = ρ * (4/3) * π * R1^3
M2 = ρ * (4/3) * π * R2^3
Comparing Gravitational Accelerations
Now we can substitute the expressions for mass into the gravity formula:
g1 = G * (ρ * (4/3) * π * R1^3) / R1^2
g2 = G * (ρ * (4/3) * π * R2^3) / R2^2
This simplifies to:
g1 = G * (ρ * (4/3) * π * R1)
g2 = G * (ρ * (4/3) * π * R2)
Now, since R1 > R2, it follows that:
g1 = (4/3) * π * G * ρ * R1
g2 = (4/3) * π * G * ρ * R2
Since R1 is greater than R2, we conclude that:
g1 > g2
Conclusion
Therefore, the correct answer is:
g1 > g2 (Option A)
This indicates that the gravitational acceleration on the surface of Planet 1 is greater than that on Planet 2, due to its larger radius while maintaining the same density.
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Suppose there are two planets, 1 and 2, having the same density but their radii are R1 and R2 respectively, where R1>R2. The accelerations due to gravity on the surface of this planet are related asa)g1 > g2b)g1 < g2c)g1 = g2d)Can’t say anythingCorrect answer is option 'A'. Can you explain this answer?
Question Description
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Suppose there are two planets, 1 and 2, having the same density but their radii are R1 and R2 respectively, where R1>R2. The accelerations due to gravity on the surface of this planet are related asa)g1 > g2b)g1 < g2c)g1 = g2d)Can’t say anythingCorrect answer is option 'A'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Suppose there are two planets, 1 and 2, having the same density but their radii are R1 and R2 respectively, where R1>R2. The accelerations due to gravity on the surface of this planet are related asa)g1 > g2b)g1 < g2c)g1 = g2d)Can’t say anythingCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Suppose there are two planets, 1 and 2, having the same density but their radii are R1 and R2 respectively, where R1>R2. The accelerations due to gravity on the surface of this planet are related asa)g1 > g2b)g1 < g2c)g1 = g2d)Can’t say anythingCorrect answer is option 'A'. Can you explain this answer?.
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