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If the radius of the earth were to shrink by one percent and its mass remains the same, the acceleration due to gravity on the earth's surface would
- a)Decrease
- b)Remain unchanged
- c)Increase
- d)Become zero
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
If the radius of the earth were to shrink by one percent and its mass ...
g = GM/R2
or g∝1/R2
g will increase if R decreases.
or g∝1/R2
g will increase if R decreases.
Most Upvoted Answer
If the radius of the earth were to shrink by one percent and its mass ...
Explanation:
When the radius of the Earth shrinks by one percent, the distance between the center of the Earth and any point on its surface decreases by one percent as well. This means that the distance from the center of the Earth to the surface decreases, resulting in a smaller radius.
The acceleration due to gravity on the surface of the Earth is given by the equation:
g = G * (M/R^2)
Where:
g is the acceleration due to gravity
G is the gravitational constant
M is the mass of the Earth
R is the radius of the Earth
Effect of Shrinking Radius:
When the radius of the Earth shrinks by one percent, the value of R in the equation decreases by one percent. Since the mass of the Earth remains the same, the value of M remains constant. Therefore, the acceleration due to gravity can be written as:
g' = G * (M/(0.99R)^2)
Comparison:
Comparing the new equation with the original equation, we can see that the new acceleration due to gravity (g') is greater than the original acceleration due to gravity (g). This means that the acceleration due to gravity on the Earth's surface increases when the radius shrinks by one percent.
Reasoning:
The reason for this increase in acceleration due to gravity can be understood by considering the inverse square relationship between the radius and the acceleration due to gravity. When the radius decreases, the distance between the center of the Earth and any point on its surface decreases. As a result, the gravitational force experienced by an object on the surface of the Earth becomes stronger, leading to an increase in acceleration due to gravity.
Therefore, the correct answer is option 'C' - the acceleration due to gravity on the Earth's surface would increase if the radius of the Earth were to shrink by one percent while its mass remains the same.
When the radius of the Earth shrinks by one percent, the distance between the center of the Earth and any point on its surface decreases by one percent as well. This means that the distance from the center of the Earth to the surface decreases, resulting in a smaller radius.
The acceleration due to gravity on the surface of the Earth is given by the equation:
g = G * (M/R^2)
Where:
g is the acceleration due to gravity
G is the gravitational constant
M is the mass of the Earth
R is the radius of the Earth
Effect of Shrinking Radius:
When the radius of the Earth shrinks by one percent, the value of R in the equation decreases by one percent. Since the mass of the Earth remains the same, the value of M remains constant. Therefore, the acceleration due to gravity can be written as:
g' = G * (M/(0.99R)^2)
Comparison:
Comparing the new equation with the original equation, we can see that the new acceleration due to gravity (g') is greater than the original acceleration due to gravity (g). This means that the acceleration due to gravity on the Earth's surface increases when the radius shrinks by one percent.
Reasoning:
The reason for this increase in acceleration due to gravity can be understood by considering the inverse square relationship between the radius and the acceleration due to gravity. When the radius decreases, the distance between the center of the Earth and any point on its surface decreases. As a result, the gravitational force experienced by an object on the surface of the Earth becomes stronger, leading to an increase in acceleration due to gravity.
Therefore, the correct answer is option 'C' - the acceleration due to gravity on the Earth's surface would increase if the radius of the Earth were to shrink by one percent while its mass remains the same.
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If the radius of the earth were to shrink by one percent and its mass remains the same, the acceleration due to gravity on the earth's surface woulda)Decreaseb)Remain unchangedc)Increased)Become zeroCorrect answer is option 'C'. Can you explain this answer?
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