Question

11. Find the gravitational potential energy of a
body of mass 10 kg when it is at a height of
6400 km from the earth's surface.
[Given : mass of the earth and radius of the
earth. See Ex. 10 above.] (Ans. - 3.127 x 108 )​

Answer 1

Explanation:

PE=mgh

=10×10×64×10^2

=64×10^4J

HOPE THIS HELPS YOU.

Answer 2

The gravitational Potential Energy is 3.127 × 10⁸ Joule

Explanation:

Given:

Mass of body = 10 kg

Mass of Earth $=6\times 10^{24}$ kg

Height of the body above the surface of the Earth = 6400 kg

Radius of the Earth = 6400 km

To find out:

Gravitational Potential Energy of the body at the height of 6400 km

Solution:

We know that Potential Energy = mgh

But this formula is applicable only for the bodies that are near the surface of the Earth where we can take g as constant

For bodies sufficiently away from the Earth, the Gravitational Potential Energy is given by

$U=-\frac{GMm}{r}$

Where r is the distance of the body from the surface of the Earth

m is the mass of the body

M is the mass of the Earth

G is gravitational constant $=6.67\times 10^{-11}$ m³ kg?¹s?²

Here,

$m = 10$ kg

$M =6\times 10^{24}$ kg

$r=6400+6400=12800$ km

Thus,

$U=-\frac{6.67\times 10^{-11}\times 6\times 10^{24}\times 10}{12800\times 10^3}$ Joule

$\implies U=-3.127\times 10^8$ Joule

Hope this answer is helpful.

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