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Show that if an object is taken to a height H above the earth's surface,it's weight decreases by the factor R²/(R+H)², where R is the radius of the earth.?
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Show that if an object is taken to a height H above the earth's surfac...
Introduction:
When an object is taken to a height above the Earth's surface, its weight decreases. This can be explained by the concept of gravitational force and the inverse square law of gravity.
Explanation:
- Gravitational force: Gravitational force is the force of attraction between two objects with mass. The force of gravity is responsible for the weight of an object. The weight of an object is the force exerted on it due to gravity.
- Inverse square law of gravity: According to the inverse square law, the force of gravity between two objects is inversely proportional to the square of the distance between their centers. Mathematically, this can be represented as F = G (m1 * m2) / r^2, where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between their centers.
Derivation:
Let's consider an object of mass m at a height H above the Earth's surface. The weight of the object at this height can be calculated using the formula W = mg, where g is the acceleration due to gravity.
- Weight at surface: The weight of the object at the Earth's surface can be given as W1 = mg1, where g1 is the acceleration due to gravity at the Earth's surface.
- Weight at height: The weight of the object at a height H above the Earth's surface can be given as W2 = mg2, where g2 is the acceleration due to gravity at that height.
Calculating the ratio:
To calculate the ratio of weight decrease, we need to find the value of g2 in terms of g1, H, and R.
- At the Earth's surface (height = 0), g1 = G (Me / R^2), where Me is the mass of the Earth.
- At a height H above the Earth's surface, g2 = G (Me / (R+H)^2).
Substituting these values into the equations for W1 and W2:
W1 = mg1 = m (G (Me / R^2))
W2 = mg2 = m (G (Me / (R+H)^2))
Taking the ratio of W2 to W1:
W2 / W1 = (m (G (Me / (R+H)^2))) / (m (G (Me / R^2)))
W2 / W1 = (Me / (R+H)^2) / (Me / R^2)
W2 / W1 = R^2 / (R+H)^2
So, if an object is taken to a height H above the Earth's surface, its weight decreases by the factor R^2 / (R+H)^2.
When an object is taken to a height above the Earth's surface, its weight decreases. This can be explained by the concept of gravitational force and the inverse square law of gravity.
Explanation:
- Gravitational force: Gravitational force is the force of attraction between two objects with mass. The force of gravity is responsible for the weight of an object. The weight of an object is the force exerted on it due to gravity.
- Inverse square law of gravity: According to the inverse square law, the force of gravity between two objects is inversely proportional to the square of the distance between their centers. Mathematically, this can be represented as F = G (m1 * m2) / r^2, where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between their centers.
Derivation:
Let's consider an object of mass m at a height H above the Earth's surface. The weight of the object at this height can be calculated using the formula W = mg, where g is the acceleration due to gravity.
- Weight at surface: The weight of the object at the Earth's surface can be given as W1 = mg1, where g1 is the acceleration due to gravity at the Earth's surface.
- Weight at height: The weight of the object at a height H above the Earth's surface can be given as W2 = mg2, where g2 is the acceleration due to gravity at that height.
Calculating the ratio:
To calculate the ratio of weight decrease, we need to find the value of g2 in terms of g1, H, and R.
- At the Earth's surface (height = 0), g1 = G (Me / R^2), where Me is the mass of the Earth.
- At a height H above the Earth's surface, g2 = G (Me / (R+H)^2).
Substituting these values into the equations for W1 and W2:
W1 = mg1 = m (G (Me / R^2))
W2 = mg2 = m (G (Me / (R+H)^2))
Taking the ratio of W2 to W1:
W2 / W1 = (m (G (Me / (R+H)^2))) / (m (G (Me / R^2)))
W2 / W1 = (Me / (R+H)^2) / (Me / R^2)
W2 / W1 = R^2 / (R+H)^2
So, if an object is taken to a height H above the Earth's surface, its weight decreases by the factor R^2 / (R+H)^2.
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Show that if an object is taken to a height H above the earth's surface,it's weight decreases by the factor R²/(R+H)², where R is the radius of the earth.?
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Show that if an object is taken to a height H above the earth's surface,it's weight decreases by the factor R²/(R+H)², where R is the radius of the earth.? 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 Show that if an object is taken to a height H above the earth's surface,it's weight decreases by the factor R²/(R+H)², where R is the radius of the earth.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Show that if an object is taken to a height H above the earth's surface,it's weight decreases by the factor R²/(R+H)², where R is the radius of the earth.?.
Show that if an object is taken to a height H above the earth's surface,it's weight decreases by the factor R²/(R+H)², where R is the radius of the earth.? 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 Show that if an object is taken to a height H above the earth's surface,it's weight decreases by the factor R²/(R+H)², where R is the radius of the earth.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Show that if an object is taken to a height H above the earth's surface,it's weight decreases by the factor R²/(R+H)², where R is the radius of the earth.?.
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