Question

If gE is acceleration due to gravity on Earth and GM is acceleration due to gravity on moon then

A.ge=gm.....
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Answer 1

Answer:

From the knowledge of theory, gm=16ge

Answer 2

Gm = $\frac{1}{6}$Ge

The net acceleration given to objects owing to the combined influence of gravitation and centrifugal force is indicated by g, the gravity of Earth. It's a vector value.

We know that,

Ge = G* $\frac{Me}{R^2}$

where G* = gravitational constant

Me = Mass of earth

R = Radius of earth

Now, Let

Gm = G* $\frac{Mm}{Rm^2}$    - (1)

where, Gm = acceleration due to gravity on moon

Mm = Mass of moon

Rm = Radius of moon

We also know,

Mm = $\frac{Me}{100}$ approx and Rm = $\frac{Re}{4}$

Substituting this in equation (1)

Gm = G* $\frac{Me/100}{(Re/4)^2}$

∴ Gm = G* $\frac{16}{100}$    $\frac{Me}{R^2}$

∴ Gm = $\frac{1}{6.25}$ G* $\frac{Me}{R^2}$

∴ Gm ≈ $\frac{1}{6}$ Ge