The gravitational potential energy of a body at a distance r from the center of the earth is U. The gravitational force at that point is?

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Solution

The Gravitational Potential Energy at a distance R is,

$U = \frac{G M m}{r}$

And weight at distance 2r is

$W = \frac{G M m}{{(2 r)}^{2}} = \frac{G M m}{4 r^{2}} = \frac{U}{4 r}$
The energy possessed by an object because of its position in the gravitational field is called Gravitational potential energy. The most common application of gravitational potential energy can be applied to the objects that are over the Earth’s surface where the gravitational acceleration can be assumed to be constant at $9.8 \times m / s e c^{2}$

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