Question

Show that the acceleration due to gravity at the surface of moon is about 1/6 of that at the surface of the earth.
Non copied answer required

Answer 1

Question :-

Show that the acceleration due to gravity at the surface of moon is about 1/6 of that at the surface of the earth.

Answer :-

let the mass of earth be M.

And the radius of earth be R.

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A/c to Newton's gravitational law,

F = GMm/R²

And,

A/c to Newton's 2nd law of motion,

F = ma

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Therefore,

acclⁿ due to gravity = (GM/R²) -----------(i)

on earth

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Now,

we know that the moon's mass is 1/81 of the the earth's mass.

And, the moon's radius is 1/4th of the earth's radius.

Thus,

mass of moon = M/81

radius of moon = R/4

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Thus,

acclⁿ due to gravity = [ (GM/81) / (R/4)² ]

on moon

= [ (GM/81) / (R²/16) ]

= GM/6R² ------------(ii)

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On dividing eqⁿ (ii) by eqⁿ (i), we get :

acclⁿ due to gravity = (1/6) × acclⁿ due to gravity

on moon on earth

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. .