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At what height from the surface of earth the value of acceleration due to gravity reduces 10% in comparison to its surface value?
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At what height from the surface of earth the value of acceleration due...
Understanding the Acceleration Due to Gravity
The acceleration due to gravity (g) at the surface of the Earth is approximately 9.81 m/s². As you move away from the Earth’s surface, this value decreases. To find the height at which g reduces by 10%, we need to understand the relationship between height and gravity.
Formula for Gravity at Height
The formula for gravitational acceleration at a height (h) above the Earth’s surface is:
- g' = g(1 - (2h/R))
Where:
- g' = acceleration due to gravity at height h
- g = acceleration due to gravity at the surface
- R = radius of the Earth (approximately 6,371 km)
Calculating the Height
To find the height where g' = 0.9g, we set up the equation:
- 0.9g = g(1 - (2h/R))
By simplifying this, we can isolate h:
- 0.9 = 1 - (2h/R)
- 2h/R = 0.1
- h = 0.05R
Now substituting R:
- h = 0.05 × 6,371 km
- h ≈ 318.55 km
Conclusion
Thus, the height from the Earth’s surface where the acceleration due to gravity reduces by 10% is approximately:
- 318.55 kilometers
This height signifies a significant altitude where the gravitational pull is noticeably less than on the surface, affecting various aspects of physics and engineering in space exploration and satellite deployment.
The acceleration due to gravity (g) at the surface of the Earth is approximately 9.81 m/s². As you move away from the Earth’s surface, this value decreases. To find the height at which g reduces by 10%, we need to understand the relationship between height and gravity.
Formula for Gravity at Height
The formula for gravitational acceleration at a height (h) above the Earth’s surface is:
- g' = g(1 - (2h/R))
Where:
- g' = acceleration due to gravity at height h
- g = acceleration due to gravity at the surface
- R = radius of the Earth (approximately 6,371 km)
Calculating the Height
To find the height where g' = 0.9g, we set up the equation:
- 0.9g = g(1 - (2h/R))
By simplifying this, we can isolate h:
- 0.9 = 1 - (2h/R)
- 2h/R = 0.1
- h = 0.05R
Now substituting R:
- h = 0.05 × 6,371 km
- h ≈ 318.55 km
Conclusion
Thus, the height from the Earth’s surface where the acceleration due to gravity reduces by 10% is approximately:
- 318.55 kilometers
This height signifies a significant altitude where the gravitational pull is noticeably less than on the surface, affecting various aspects of physics and engineering in space exploration and satellite deployment.
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At what height from the surface of earth the value of acceleration due to gravity reduces 10% in comparison to its surface value?
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At what height from the surface of earth the value of acceleration due to gravity reduces 10% in comparison to its surface value? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about At what height from the surface of earth the value of acceleration due to gravity reduces 10% in comparison to its surface value? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At what height from the surface of earth the value of acceleration due to gravity reduces 10% in comparison to its surface value?.
At what height from the surface of earth the value of acceleration due to gravity reduces 10% in comparison to its surface value? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about At what height from the surface of earth the value of acceleration due to gravity reduces 10% in comparison to its surface value? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At what height from the surface of earth the value of acceleration due to gravity reduces 10% in comparison to its surface value?.
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