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If the mass of the earth is not changed and its radius decreased by 1% then the acceleration due to gravity on the surface of the earth would be:
- a)Increase by 2 %
- b)Decrease by 2 %
- c)Increase by 9.8 %
- d)Remains unchanged
Correct answer is option 'A'. Can you explain this answer?
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Understanding Acceleration Due to Gravity
The acceleration due to gravity (g) at the surface of a planet is given by the formula:
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.
Impact of Decreasing the Radius
When the radius of the Earth decreases by 1%, we can analyze the effect on gravity:
- New Radius (R'): If R is decreased by 1%, then R' = R * (1 - 0.01) = 0.99R.
Calculating the New Acceleration Due to Gravity
Using the modified radius in the formula for g,
- New g (g'):
g' = G * M / (0.99R)^2
This simplifies to:
g' = G * M / (0.9801R^2)
- Comparing g and g':
g' = g / 0.9801
Change in Acceleration Due to Gravity
Now, let's calculate the percentage change in gravity:
- Percentage Increase:
1 - (1 / 0.9801) = 0.0204 or approximately 2%.
Thus, the new acceleration due to gravity increases by about 2%.
Conclusion
With a decrease in the radius of the Earth by 1%, the acceleration due to gravity increases by approximately 2%. Therefore, the correct answer is option 'A'.
The acceleration due to gravity (g) at the surface of a planet is given by the formula:
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.
Impact of Decreasing the Radius
When the radius of the Earth decreases by 1%, we can analyze the effect on gravity:
- New Radius (R'): If R is decreased by 1%, then R' = R * (1 - 0.01) = 0.99R.
Calculating the New Acceleration Due to Gravity
Using the modified radius in the formula for g,
- New g (g'):
g' = G * M / (0.99R)^2
This simplifies to:
g' = G * M / (0.9801R^2)
- Comparing g and g':
g' = g / 0.9801
Change in Acceleration Due to Gravity
Now, let's calculate the percentage change in gravity:
- Percentage Increase:
1 - (1 / 0.9801) = 0.0204 or approximately 2%.
Thus, the new acceleration due to gravity increases by about 2%.
Conclusion
With a decrease in the radius of the Earth by 1%, the acceleration due to gravity increases by approximately 2%. Therefore, the correct answer is option 'A'.
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If the mass of the earth is not changed and its radius decreased by 1% then the acceleration due to gravity on the surface of the earth would be:a)Increase by 2 %b)Decrease by 2 %c)Increase by 9.8 %d)Remains unchangedCorrect answer is option 'A'. Can you explain this answer?
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If the mass of the earth is not changed and its radius decreased by 1% then the acceleration due to gravity on the surface of the earth would be:a)Increase by 2 %b)Decrease by 2 %c)Increase by 9.8 %d)Remains unchangedCorrect answer is option 'A'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about If the mass of the earth is not changed and its radius decreased by 1% then the acceleration due to gravity on the surface of the earth would be:a)Increase by 2 %b)Decrease by 2 %c)Increase by 9.8 %d)Remains unchangedCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the mass of the earth is not changed and its radius decreased by 1% then the acceleration due to gravity on the surface of the earth would be:a)Increase by 2 %b)Decrease by 2 %c)Increase by 9.8 %d)Remains unchangedCorrect answer is option 'A'. Can you explain this answer?.
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If the mass of the earth is not changed and its radius decreased by 1% then the acceleration due to gravity on the surface of the earth would be:a)Increase by 2 %b)Decrease by 2 %c)Increase by 9.8 %d)Remains unchangedCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for If the mass of the earth is not changed and its radius decreased by 1% then the acceleration due to gravity on the surface of the earth would be:a)Increase by 2 %b)Decrease by 2 %c)Increase by 9.8 %d)Remains unchangedCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of If the mass of the earth is not changed and its radius decreased by 1% then the acceleration due to gravity on the surface of the earth would be:a)Increase by 2 %b)Decrease by 2 %c)Increase by 9.8 %d)Remains unchangedCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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