If a person weights 750 N on Earth, how much would be his weight on the Moon given that Moon's mass is `1/81` of that of the Earth andits radius is `1/3.7` of that of Earth.

Explanation

Given: Weight on Earth `(W_(E))=750N`
`M_(m)=1/81M_(E)=:.((M_(m))/(M_(E)))=1/81`
`R_(m)=1/3.7R_(E):((R_(m))/(R_(E)))=1/3.7`
To find: Weight on Moon `(W_(m))=?`
Formula: `W=F=(GMm)/(R^(2))`
Solution
For Earth
`W_(E)=(GM_(E)m)/(R_(E)^(2))`.............i
For Moon
`W_(m)=(GM_(m)m)/(R_(m)^(2))`........ii
Diving equation ii by i
`(W_(M))/(W_(E))=(GM_(m)m)/(R_(m)^(2))-:(GM_(E)m)/(R_(E)^(2))`
`(W_(M))/(W_(E))=(GM_(m)m)/(R_(m)^(2))xx(R_(E)^(2))/(GM_(E)m)`
`(W_(M))/(W_(E))=(M_(m))/(M_(E))xx[(R_(E))/(R_(m))]^(2)`
`(W_(m))/750=1/81xx(3.7)^(2)`..........from given
`(W_(m))/750\13.69/81`
`W_(m)=13.69xx750/81`
`W_(m)=126.8N`
The weight on the Moon is 126.8N.