Class 11 Exam > Class 11 Questions > If the radius of the earth decreases by 10%, ...
Start Learning for Free
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?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
If the radius of the earth decreases by 10%, the massremaining unchang...
Free Test
FREE
| Start Free Test |
Community Answer
If the radius of the earth decreases by 10%, the massremaining unchang...
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'.
Attention Class 11 Students!
To make sure you are not studying endlessly, EduRev has designed Class 11 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 11.
|
Explore Courses for Class 11 exam
|
|
Similar Class 11 Doubts
Top Courses for Class 11View all
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?
Question Description
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? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about 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? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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?.
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? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about 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? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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?.
Solutions for 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? in English & in Hindi are available as part of our courses for Class 11.
Download more important topics, notes, lectures and mock test series for Class 11 Exam by signing up for free.
Here you can find the meaning of 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? defined & explained in the simplest way possible. Besides giving the explanation of
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?, a detailed solution for 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? has been provided alongside types of 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? theory, EduRev gives you an
ample number of questions to practice 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? tests, examples and also practice Class 11 tests.
|
|
Explore Courses for Class 11 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup