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Calculate the height of the point vertically above the Earth's surface at the which the value of acceleration due to gravity is reduced to one - fourth of its value at the surface of the earth given that radius of the earth =6400 km?
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Calculate the height of the point vertically above the Earth's surface...
2400km. apply formulae g'=g(1-2h/R) where r is radius of Earth and g'=g/4
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Calculate the height of the point vertically above the Earth's surface...
Given:
Radius of the Earth (r) = 6400 km
To find:
Height (h) at which acceleration due to gravity is reduced to one-fourth of its value at the surface of the Earth.
Formula:
The formula to calculate the acceleration due to gravity at a certain height above the Earth's surface is given by:
g' = (g * (r / (r + h)))^2
Where:
g' = acceleration due to gravity at height h
g = acceleration due to gravity at the surface of the Earth
r = radius of the Earth
h = height above the Earth's surface
Solution:
To find the height at which the acceleration due to gravity is reduced to one-fourth, we need to substitute the given values into the formula.
Let's assume the acceleration due to gravity at the surface of the Earth is g.
So, g' = (g * (r / (r + h)))^2
Given that g' = (1/4)g, we can substitute this value into the equation:
(1/4)g = (g * (r / (r + h)))^2
Taking the square root of both sides, we get:
√((1/4)g) = g * (r / (r + h))
Simplifying further:
√(1/4) = r / (r + h)
1/2 = r / (r + h)
Cross-multiplying:
r = (r + h) / 2
2r = r + h
h = 2r - r
h = r
Therefore, the height at which the acceleration due to gravity is reduced to one-fourth of its value at the surface of the Earth is equal to the radius of the Earth, which is 6400 km.
Radius of the Earth (r) = 6400 km
To find:
Height (h) at which acceleration due to gravity is reduced to one-fourth of its value at the surface of the Earth.
Formula:
The formula to calculate the acceleration due to gravity at a certain height above the Earth's surface is given by:
g' = (g * (r / (r + h)))^2
Where:
g' = acceleration due to gravity at height h
g = acceleration due to gravity at the surface of the Earth
r = radius of the Earth
h = height above the Earth's surface
Solution:
To find the height at which the acceleration due to gravity is reduced to one-fourth, we need to substitute the given values into the formula.
Let's assume the acceleration due to gravity at the surface of the Earth is g.
So, g' = (g * (r / (r + h)))^2
Given that g' = (1/4)g, we can substitute this value into the equation:
(1/4)g = (g * (r / (r + h)))^2
Taking the square root of both sides, we get:
√((1/4)g) = g * (r / (r + h))
Simplifying further:
√(1/4) = r / (r + h)
1/2 = r / (r + h)
Cross-multiplying:
r = (r + h) / 2
2r = r + h
h = 2r - r
h = r
Therefore, the height at which the acceleration due to gravity is reduced to one-fourth of its value at the surface of the Earth is equal to the radius of the Earth, which is 6400 km.
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Calculate the height of the point vertically above the Earth's surface at the which the value of acceleration due to gravity is reduced to one - fourth of its value at the surface of the earth given that radius of the earth =6400 km?
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Calculate the height of the point vertically above the Earth's surface at the which the value of acceleration due to gravity is reduced to one - fourth of its value at the surface of the earth given that radius of the earth =6400 km? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Calculate the height of the point vertically above the Earth's surface at the which the value of acceleration due to gravity is reduced to one - fourth of its value at the surface of the earth given that radius of the earth =6400 km? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Calculate the height of the point vertically above the Earth's surface at the which the value of acceleration due to gravity is reduced to one - fourth of its value at the surface of the earth given that radius of the earth =6400 km?.
Calculate the height of the point vertically above the Earth's surface at the which the value of acceleration due to gravity is reduced to one - fourth of its value at the surface of the earth given that radius of the earth =6400 km? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Calculate the height of the point vertically above the Earth's surface at the which the value of acceleration due to gravity is reduced to one - fourth of its value at the surface of the earth given that radius of the earth =6400 km? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Calculate the height of the point vertically above the Earth's surface at the which the value of acceleration due to gravity is reduced to one - fourth of its value at the surface of the earth given that radius of the earth =6400 km?.
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