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If the radius of the earth decreases by 10%, the massremaining unchanged, what will happen to theacceleration due to gravity?
- a)Decreases by 19%
- b)Increases by 19%
- c)Decreases by more than 19%
- d)Increases by more than 19%
Correct answer is option 'D'. Can you explain this answer?
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Explanation:
When the radius of the Earth decreases by 10%, the mass remains unchanged. We need to determine the effect of this change on the acceleration due to gravity.
Formula:
The acceleration due to gravity can be calculated using the formula:
g = G * (M / R^2)
Where:
g is the acceleration due to gravity
G is the universal gravitational constant
M is the mass of the Earth
R is the radius of the Earth
Effect of Decreased Radius:
When the radius of the Earth decreases by 10%, the new radius can be calculated as:
New Radius = (100% - 10%) * Old Radius = 90% * Old Radius
Effect on Acceleration due to Gravity:
Substituting the new radius into the formula, we get:
New g = G * (M / (0.9 * R)^2)
Simplifying the expression, we have:
New g = G * (M / (0.81 * R^2))
Comparing this with the original formula, we can see that the new acceleration due to gravity is smaller than the original value. This means that the acceleration due to gravity decreases when the radius of the Earth decreases.
Percentage Change:
To determine the percentage change in the acceleration due to gravity, we can calculate the difference between the new and original values and express it as a percentage of the original value:
Percentage Change = ((Original g - New g) / Original g) * 100%
Substituting the values, we have:
Percentage Change = ((G * (M / R^2) - G * (M / (0.81 * R^2))) / (G * (M / R^2))) * 100%
Simplifying further, we get:
Percentage Change = (1 - 0.81) / 0.81 * 100%
Percentage Change = (0.19 / 0.81) * 100%
Percentage Change ≈ 23.5%
Therefore, the acceleration due to gravity decreases by more than 19% when the radius of the Earth decreases by 10%. The correct answer is option 'D'.
When the radius of the Earth decreases by 10%, the mass remains unchanged. We need to determine the effect of this change on the acceleration due to gravity.
Formula:
The acceleration due to gravity can be calculated using the formula:
g = G * (M / R^2)
Where:
g is the acceleration due to gravity
G is the universal gravitational constant
M is the mass of the Earth
R is the radius of the Earth
Effect of Decreased Radius:
When the radius of the Earth decreases by 10%, the new radius can be calculated as:
New Radius = (100% - 10%) * Old Radius = 90% * Old Radius
Effect on Acceleration due to Gravity:
Substituting the new radius into the formula, we get:
New g = G * (M / (0.9 * R)^2)
Simplifying the expression, we have:
New g = G * (M / (0.81 * R^2))
Comparing this with the original formula, we can see that the new acceleration due to gravity is smaller than the original value. This means that the acceleration due to gravity decreases when the radius of the Earth decreases.
Percentage Change:
To determine the percentage change in the acceleration due to gravity, we can calculate the difference between the new and original values and express it as a percentage of the original value:
Percentage Change = ((Original g - New g) / Original g) * 100%
Substituting the values, we have:
Percentage Change = ((G * (M / R^2) - G * (M / (0.81 * R^2))) / (G * (M / R^2))) * 100%
Simplifying further, we get:
Percentage Change = (1 - 0.81) / 0.81 * 100%
Percentage Change = (0.19 / 0.81) * 100%
Percentage Change ≈ 23.5%
Therefore, the acceleration due to gravity decreases by more than 19% when the radius of the Earth decreases by 10%. The correct answer is option 'D'.
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If the radius of the earth decreases by 10%, the massremaining unchanged, what will happen to theacceleration due to gravity?a)Decreases by 19%b)Increases by 19%c)Decreases by more than 19%d)Increases by more than 19%Correct answer is option 'D'. Can you explain this answer?
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