Question

If a person weighs 750 N on Earth, what will be the weight of the person on the Moon?

(The mass of moon is `1/81` times the mass earth and its radius is `1/3.7` times that of earth.)

Answer 1

Given:

Weight on earth = 750 N, 
Ratio of mass of the earth (M_E) to mass of the moon (M_M)

`= "M"_"E"/"M"_"M"` = 81

Ratio of radius of the earth (R_E) to radius of moon (R_M)

`= "R"_"E"/"R"_"M"` = 3.7

To find:

Weight on moon (W_moon)

Weight = mg = `"mGM"/"R"^2"`   ...[Formula]

Weight on the Earth,

mg = `"mGM"_"E"/"R"_"E"^2`

= 750

∴ m = `(750  "R"_"E"^2)/(("GM"_"E"))`   ...[i]

Weight on Moon,

`"W"_"moon" = "mGM"_"M"/"R"_"M"^2`   ....[ii]

Substituting equation [i] in equation [ii],

`"W"_"moon" = (750  "R"_"E"^2)/(("GM"_"E")) xx "GM"_"M"/"R"_"M"^2`

`= 750  "R"_"E"^2/"R"_"M"^2 xx "M"_"M"/"M"_"E"`

`"W"_"moon" = 750 xx (3.7)^2 xx 1/81`

= 126.8 N

The weight of the person on the moon will be 126.8 N.