If an object is near the surface of the earth, the variation of its weight with

Question

If an object is near the surface of the earth, the variation of its weight with distance from the center of the earth can often be neglected. The accelertaion due to gravity at sea level is 9.81 m/s^2. The radius of the earth is 6370 km. The weight of an object at sea level is mg, where m is its mass. At what height above the surface of the earth does the weight of the object decrease to 0.99mg? If an object is near the surface of the earth, the variation of its weight with distance from the center of the earth can often be neglected. The accelertaion due to gravity at sea level is 9.81 m/s^2. The radius of the earth is 6370 km. The weight of an object at sea level is mg, where m is its mass. At what height above the surface of the earth does the weight of the object decrease to 0.99mg? If an object is near the surface of the earth, the variation of its weight with distance from the center of the earth can often be neglected. The accelertaion due to gravity at sea level is 9.81 m/s^2. The radius of the earth is 6370 km. The weight of an object at sea level is mg, where m is its mass. At what height above the surface of the earth does the weight of the object decrease to 0.99mg?

Explanation / Answer

weight of an object is the gravitational force exerted by earth on the object

W1 = G*M*m/R^2 = mg

W2 = G*M*m/(R+h)^2 = 0.99mg

W2 / w1

(R/(R+h))^2 = 0.99

(6370/(6370+h))^2 = 0.99

h = 32.1 km <<--------------answer

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