What is the weight of a body having a mass of 100 kg at a height of 3200 km far from the earths surface if the mass of the earth is 6*10^24kg and its radius is 6400km?
Answers
Explanation:
Let g’ be the value of g at a height h above the surface of the earth. Then,
g’=GM/(R+h)^2
where R is the radius of the earth. This can also be written as
g’=(GM/R^2)/(1+h/R)^2 = g/(1+h/R)^2
where g is the value of f at the earth’s surface. Here g is given by
g=6.67*10^-11*6*10^24/6400000^2 = 9.776 m/s^2
So,
h’=9.776/(1+3200/6400)^2 = 4.345 m/s^2
Weight of the body of mass 100 kg at a height of 3200 km= 434.5 Newtons.....
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Answer:
The weight of an object on, for example, a planet, is inversely proportion to the square of the distance from the object to the center of gravity of the planet. I realize that for those who are not mathematically inclined, the above description may be lacking in clarity. So, let me illustrate it a couple of examples.
An object weight 90 kilograms on the surface of the earth (6400 km from the center of the earth). Triple this distance. He is now 19,200 km from the center of the earth (and 12,800 km above its surface). The rule is inverse-square. So, the ratio if 19,200 / 6400 or 3 /1. Take the inverse: 1 / 3. Now square this and you will get 1/3 * 1/3 or 1/9. The object will weigh one ninth as much as on thee surface of the earth. One ninth of 90 kg is 10 kg.
An object weight 242 pounds on the surface of the earth (4000 miles from the center of the earth). How much would he weigh on an “elevated platform” 400 miles above the surface of the earth? Solution: He is 400 miles above the surface and an additional 4000 miles from the earth’s center. He is therefore, 4400 miles above the center of the earth. The rule is inverse-square. So, the ratio if 4400 / 4000 or 11/10. Take the inverse: 10 / 11. Now square this and you will get 10/11 * 10/11 or 100/121. The object will weigh 100/121 as much as on the surface of the earth. Now 100/121 of 242 pounds is 200 pounds.
Now for the given problem:
An object weight 100 kilograms on the surface of the earth (6400 km from the center of the earth). He is now 9600 km from the center of the earth (3200 km above the surface and 6400 km more to the center of the earth). The rule is inverse-square. So, the ratio if 9600 / 6400 or 3 /2. Take the inverse: 2 / 3. Now square this and you will get 2/3 * 2/3 or 4/9. The object will weigh four ninths as much as on the surface of the earth. Four ninths of 100 kg is 44 4/9 kg. This may be rounded to 44.4 kg (if you like).