Question

Raju weighs 800 N on earth. How much would be his weight on the moon given that the moon's mass is `1/81` of that of the earth and its radius is `1/3.7` of that of the earth?

Answer 1

Weight of Raju on earth = 800 N

Ratio of mass of the moon (M_M) to mass of the earth (M_E) = `("M"_"M")/("M"_"E")`

Ratio of radius of moon (R_M) to radius of earth (R_E) = `("R"_"M")/("R"_"E")`

Let the mass of the person be m kg.

Weight on the earth = mg = 800 = `(("mGM"_"E"))/"R"_"E"^2` .....`(∵ "g" = ("GM"_"E")/("R"_"E"^2))`

Therefore, m = `(800 "R"_"E"^2)/("GM"_"E")` ........(i)

Weight on moon = `("mGM"_"M")/("R"_"M"^2)`

= `(800 "R"_"E"^2)/(("GM"_"E")) xx "GM"_"M"/"R"_"M"^2` ........[Using (i)]

= `800 xx "R"_"E"^2/"R"_"M"^2 xx "M"_"M"/"M"_"E"`

= `800 xx (3.7)^2 xx 1/81`

= 135.2 N