NEET Exam > NEET Questions > The height above surface of earth where the v...
Start Learning for Free
The height above surface of earth where the value of gravitational acceleration is one fourth of that at surface, will be
- a)Re/4
- b)Re/2
- c)3Re/4
- d)Re
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The height above surface of earth where the value of gravitational acc...
Understanding Gravitational Acceleration
Gravitational acceleration at the surface of the Earth (g) is approximately 9.81 m/s². As you move away from the Earth's surface, gravitational acceleration decreases according to the formula:
g' = g / (1 + h/R)²
Where:
- g' is the gravitational acceleration at height h,
- g is the gravitational acceleration at the surface (9.81 m/s²),
- R is the radius of the Earth (approximately 6400 km),
- h is the height above the surface.
Condition for One Fourth of Surface Gravity
To find the height where gravitational acceleration is one fourth of that at the surface, we set up the equation:
g' = g/4
Substituting the formula:
g / (1 + h/R)² = g/4
This simplifies to:
1 / (1 + h/R)² = 1/4
Taking the square root of both sides gives:
1/(1 + h/R) = 1/2
From this, we can derive:
1 + h/R = 2
This leads to:
h/R = 2 - 1
Thus,
h/R = 1
h = R
Conclusion: Height Above Earth's Surface
The height at which gravitational acceleration is one fourth of that at the Earth's surface is equal to the radius of the Earth (R). Therefore, the correct answer is:
Option D: Re
Gravitational acceleration at the surface of the Earth (g) is approximately 9.81 m/s². As you move away from the Earth's surface, gravitational acceleration decreases according to the formula:
g' = g / (1 + h/R)²
Where:
- g' is the gravitational acceleration at height h,
- g is the gravitational acceleration at the surface (9.81 m/s²),
- R is the radius of the Earth (approximately 6400 km),
- h is the height above the surface.
Condition for One Fourth of Surface Gravity
To find the height where gravitational acceleration is one fourth of that at the surface, we set up the equation:
g' = g/4
Substituting the formula:
g / (1 + h/R)² = g/4
This simplifies to:
1 / (1 + h/R)² = 1/4
Taking the square root of both sides gives:
1/(1 + h/R) = 1/2
From this, we can derive:
1 + h/R = 2
This leads to:
h/R = 2 - 1
Thus,
h/R = 1
h = R
Conclusion: Height Above Earth's Surface
The height at which gravitational acceleration is one fourth of that at the Earth's surface is equal to the radius of the Earth (R). Therefore, the correct answer is:
Option D: Re
Free Test
FREE
| Start Free Test |
Community Answer
The height above surface of earth where the value of gravitational acc...
To find the height above the Earth's surface where the gravitational acceleration is one-fourth of its value at the surface, we can use the formula for gravitational acceleration:
Thus, the height at which the gravitational acceleration is one-fourth of that at the Earth's surface is Re.
|
Explore Courses for NEET exam
|
|
Top Courses for NEETView all
Question Description
The height above surface of earth where the value of gravitational acceleration is one fourth of that at surface, will bea)Re/4b)Re/2c)3Re/4d)ReCorrect answer is option 'D'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The height above surface of earth where the value of gravitational acceleration is one fourth of that at surface, will bea)Re/4b)Re/2c)3Re/4d)ReCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The height above surface of earth where the value of gravitational acceleration is one fourth of that at surface, will bea)Re/4b)Re/2c)3Re/4d)ReCorrect answer is option 'D'. Can you explain this answer?.
The height above surface of earth where the value of gravitational acceleration is one fourth of that at surface, will bea)Re/4b)Re/2c)3Re/4d)ReCorrect answer is option 'D'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The height above surface of earth where the value of gravitational acceleration is one fourth of that at surface, will bea)Re/4b)Re/2c)3Re/4d)ReCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The height above surface of earth where the value of gravitational acceleration is one fourth of that at surface, will bea)Re/4b)Re/2c)3Re/4d)ReCorrect answer is option 'D'. Can you explain this answer?.
Solutions for The height above surface of earth where the value of gravitational acceleration is one fourth of that at surface, will bea)Re/4b)Re/2c)3Re/4d)ReCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for NEET.
Download more important topics, notes, lectures and mock test series for NEET Exam by signing up for free.
Here you can find the meaning of The height above surface of earth where the value of gravitational acceleration is one fourth of that at surface, will bea)Re/4b)Re/2c)3Re/4d)ReCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The height above surface of earth where the value of gravitational acceleration is one fourth of that at surface, will bea)Re/4b)Re/2c)3Re/4d)ReCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for The height above surface of earth where the value of gravitational acceleration is one fourth of that at surface, will bea)Re/4b)Re/2c)3Re/4d)ReCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of The height above surface of earth where the value of gravitational acceleration is one fourth of that at surface, will bea)Re/4b)Re/2c)3Re/4d)ReCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The height above surface of earth where the value of gravitational acceleration is one fourth of that at surface, will bea)Re/4b)Re/2c)3Re/4d)ReCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice NEET tests.
|
|
Explore Courses for NEET exam
|
|
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!
within 7 days!
Takes less than 10 seconds to signup