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A person can jump $1 m$ on the surface of the earth. On the surface of the moon, it can jump to [[1]] m.

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Detailed Solution

A person can jump

1 m

on the surface of the earth. On the surface of the moon, it can jump to

6 m

.
Because the moon is

100 times

less massive than the Earth and has a radius

4 times

lesser than the earth’s radius. That's why its gravity is one-sixth that of the earth.
Since

g_{moon} = {\frac{G M_{m}}{{R_{m}}^{2}}}_{} = \frac{G M_{e}}{100 {(\frac{R_{e}}{4})}^{2}}

M_{m} = \frac{M_{e}}{100}

and

R_{m} = \frac{R_{e}}{4}

gmoon = moon’s gravity

{M_{m}}_{}

= mass of the moon

M_{e}

= mass of the earth

R_{m}

= radius of the moon

R_{e}

= radius of the earth

g_{moon} = \frac{16 G M_{e}}{100 R_{e}^{2}}

— eqn (1)

g_{earth} = \frac{G {M_{e}}_{}}{R_{e}^{2}}

— eqn (2)
On dividing eqn 1 by eqn 2, We get

g_{moon} = \frac{1}{6} g_{earth}

So the force exerted by the moon on the object is one-sixth as compared to the force exerted by the earth. That's why a person can jump up to

6 times

as that on earth.

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