The gravitational field strength of the earth at a point on the earth’s surface is given as *1 pointGM/R^2GMm/R^2GM/RGMm/R
Question
The gravitational field strength of the earth at a point on the earth's surface is given as
*1 pointGM/R^2
GMm/R^2
GM/R
GMm/R
Solution
The gravitational field strength of the earth at a point on the earth’s surface is given as GM/R^2.
Here's why:
- G is the gravitational constant.
- M is the mass of the Earth.
- R is the distance from the center of the Earth to the point on the surface.
The formula GM/R^2 is derived from Newton's law of universal gravitation, which states that every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
When we talk about the gravitational field strength at a point on the Earth's surface, we're interested in the force per unit mass (since field strength is defined as force per unit mass). So we're looking at the force between the Earth and a unit mass at that point.
The force between the Earth and the unit mass would be given by GMm/R^2 (where m is the mass of the object), but since we're looking at a unit mass, m is 1 and the formula simplifies to GM/R^2.
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