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The acceleration due to gravity near the Earth's surface is 9.8 m/s2, and the Earth's radius is 6,400km.From this data calculate the mass of the earth.Use any universal constant if required.?
Verified Answer
The acceleration due to gravity near the Earth's surface is 9.8 m/s2, ...
we know
g = GM/R^2
where g = acceleration due to gravity
G = Gravitational constant
M = mass of earth
R = radius of earth
g = GM/R^2
M = gR^2/G
M = 9.8 x 6.4 x 10^12 / 6.67 x 10 -11
M = 6.018 x 10^24 kg
This question is part of UPSC exam. View all Class 9 courses
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The acceleration due to gravity near the Earth's surface is 9.8 m/s2, ...
Calculating the Mass of the Earth
The mass of the Earth can be determined by using the acceleration due to gravity near the Earth's surface and the Earth's radius. The formula to calculate the mass of an object using acceleration due to gravity is:
Mass = (Acceleration due to gravity * Radius^2) / Gravitational constant
Let's break down the calculation step by step:
Step 1: Convert the radius of the Earth to meters
Given that the Earth's radius is 6,400 km, we need to convert it to meters:
Radius = 6,400 km * 1,000 m/km = 6,400,000 meters
Step 2: Calculate the mass of the Earth
Using the formula mentioned above:
Mass = (Acceleration due to gravity * Radius^2) / Gravitational constant
Acceleration due to gravity near the Earth's surface is given as 9.8 m/s^2.
The gravitational constant is denoted by G and its value is approximately 6.67430 x 10^-11 N(m/kg)^2.
Substituting the values into the formula:
Mass = (9.8 m/s^2 * (6,400,000 meters)^2) / (6.67430 x 10^-11 N(m/kg)^2)
By performing the calculations, we can determine the mass of the Earth.
Final Answer:
The mass of the Earth is approximately 5.972 x 10^24 kg.
Please note that the above calculation assumes a simplified model of the Earth and does not take into account variations in the gravitational field or the Earth's shape. However, for most practical purposes, this approximation is sufficient.
The mass of the Earth can be determined by using the acceleration due to gravity near the Earth's surface and the Earth's radius. The formula to calculate the mass of an object using acceleration due to gravity is:
Mass = (Acceleration due to gravity * Radius^2) / Gravitational constant
Let's break down the calculation step by step:
Step 1: Convert the radius of the Earth to meters
Given that the Earth's radius is 6,400 km, we need to convert it to meters:
Radius = 6,400 km * 1,000 m/km = 6,400,000 meters
Step 2: Calculate the mass of the Earth
Using the formula mentioned above:
Mass = (Acceleration due to gravity * Radius^2) / Gravitational constant
Acceleration due to gravity near the Earth's surface is given as 9.8 m/s^2.
The gravitational constant is denoted by G and its value is approximately 6.67430 x 10^-11 N(m/kg)^2.
Substituting the values into the formula:
Mass = (9.8 m/s^2 * (6,400,000 meters)^2) / (6.67430 x 10^-11 N(m/kg)^2)
By performing the calculations, we can determine the mass of the Earth.
Final Answer:
The mass of the Earth is approximately 5.972 x 10^24 kg.
Please note that the above calculation assumes a simplified model of the Earth and does not take into account variations in the gravitational field or the Earth's shape. However, for most practical purposes, this approximation is sufficient.
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The acceleration due to gravity near the Earth's surface is 9.8 m/s2, and the Earth's radius is 6,400km.From this data calculate the mass of the earth.Use any universal constant if required.?
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The acceleration due to gravity near the Earth's surface is 9.8 m/s2, and the Earth's radius is 6,400km.From this data calculate the mass of the earth.Use any universal constant if required.? 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 The acceleration due to gravity near the Earth's surface is 9.8 m/s2, and the Earth's radius is 6,400km.From this data calculate the mass of the earth.Use any universal constant if required.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The acceleration due to gravity near the Earth's surface is 9.8 m/s2, and the Earth's radius is 6,400km.From this data calculate the mass of the earth.Use any universal constant if required.?.
The acceleration due to gravity near the Earth's surface is 9.8 m/s2, and the Earth's radius is 6,400km.From this data calculate the mass of the earth.Use any universal constant if required.? 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 The acceleration due to gravity near the Earth's surface is 9.8 m/s2, and the Earth's radius is 6,400km.From this data calculate the mass of the earth.Use any universal constant if required.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The acceleration due to gravity near the Earth's surface is 9.8 m/s2, and the Earth's radius is 6,400km.From this data calculate the mass of the earth.Use any universal constant if required.?.
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