03. Acceleration due to gravity on the surface of
earth is given by s=G
where G is the gravitational constant, M is the
mass of earth and R is the radius of earth. Using
the method of dimensional analysis whether
the relation is correct.
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As we all learned in grade school, the Earth is the third planet from the Sun. The planet Earth is only a tiny part of the universe, but it is the home of human beings and all known life in it. Animals, plants and other organisms live almost everywhere on Earth's surface. It ranks fifth in size, and its mass is found to be about 5.98 × 1024 kg. Mass is a characteristic that is inherent, and it is independent of the object's environment and the method used to measure it. It is a scalar quantity, that is, a single value with and appropriate unit that has no direction.
The mass of the Earth may be determined using Newton's law of gravitation. It is given as the force (F), which is equal to the Gravitational constant multiplied by the mass of the planet and the mass of the object, divided by the square of the radius of the planet. We set this equal to the fundamental equation, force (F) equals mass (m) multiplied by acceleration (a). We know that the acceleration due to gravity is equal to 9.8 m/s2, the Gravitational constant (G) is 6.673 × 10−11 Nm2/kg2, the radius of the Earth is 6.37 × 106 m, and mass cancels out. When we rearrange the equation and plug all the numbers in, we find that the mass of the Earth is 5.96 × 1024 kg.
F = Gm1m2/r2 = ma
Gm/r2 = g
m = gr2/G
m = (9.8 m/s2)(6.37 × 106 m)2/(6.673 × 10−11 Nm2/kg2)
m = 5.96 × 1024 kg
The Earth gains mass each day, as a result of incoming debris from space. This occurs in the forms of "falling stars", or meteors, on a dark night. The actual amount of added material depends on each study, though it is estimated that 10 to the 8th power kilograms of in-falling matter accumulates every day. The seemingly large amount, however, is insignificant to the Earth's total mass. The Earth adds an estimated one quadrillionth of one percent to its weight each day.
Earth, the third planet from the sun, is one of the most unique celestial bodies in our solar system. It is the only planet in our solar system that sustains life and it is the planet that we can call our own.
In approximately 230 BC, the Greek mathematian, Eratosthenes calulated the radius of the Earth. He compared the shadows in the wells during the summer solstice and obtained the value 6.38 × 106 M. In the 16th century, Galileo determined the acceleration due to the force of gravity near the surface of the Earth and obtained 9.8 m/sec2.
The mass of the Earth may be determined using Newton's law of gravitation. It is given as the force (F), which is equal to the Gravitational constant multiplied by the mass of the planet and the mass of the object, divided by the square of the radius of the planet. We set this equal to the fundamental equation, force (F) equals mass (m) multiplied by acceleration (a). We know that the acceleration due to gravity is equal to 9.8 m/s2, the Gravitational constant (G) is 6.673 × 10−11 Nm2/kg2, the radius of the Earth is 6.37 × 106 m, and mass cancels out. When we rearrange the equation and plug all the numbers in, we find that the mass of the Earth is 5.96 × 1024 kg.
F = Gm1m2/r2 = ma
Gm/r2 = g
m = gr2/G
m = (9.8 m/s2)(6.37 × 106 m)2/(6.673 × 10−11 Nm2/kg2)
m = 5.96 × 1024 kg
The Earth gains mass each day, as a result of incoming debris from space. This occurs in the forms of "falling stars", or meteors, on a dark night. The actual amount of added material depends on each study, though it is estimated that 10 to the 8th power kilograms of in-falling matter accumulates every day. The seemingly large amount, however, is insignificant to the Earth's total mass. The Earth adds an estimated one quadrillionth of one percent to its weight each day.
Earth, the third planet from the sun, is one of the most unique celestial bodies in our solar system. It is the only planet in our solar system that sustains life and it is the planet that we can call our own.
In approximately 230 BC, the Greek mathematian, Eratosthenes calulated the radius of the Earth. He compared the shadows in the wells during the summer solstice and obtained the value 6.38 × 106 M. In the 16th century, Galileo determined the acceleration due to the force of gravity near the surface of the Earth and obtained 9.8 m/sec2.
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