The radius of earth is about `6400Km` and that of mars is about `3200 km` The mass of the earth is about `10`times the mass of mars. An object weight `200N` on earth 's surface, then its weight on the surface of mars will be:

Options

A. `8N`
B. `80N`
C. `40N`
D. `20N`

Answer

A

Explanation

According to the law of gravitation,
`F=G (M_(e)m)/(R_(e)^(2))`........(i)
Also from Newton's second law,we have
`mg=F........(ii)`
`:. mg=G(M_(e)m)/(R_(e)^(2))`.......(iii)
`(w_(e))/(w_(m))=(mg_(e))/(mg_(m)) =(M_(e))/(M_(m))((R_(m))/(R_(e)))^(2)`
where `g_(e),g_(m)` are gravity on earth and moon respectively. Also `M_(e)` and `M_(m)` are masses of moon and earth, and `R_(e)` and `R_(m)` their radii.
Given, `R_(e)=6400km, R_(m)=3200km`,
`(M_(e))/(M_(m))=10, w_(e)=200N`
`:. w_(m)=1/10(6400/(3200))^(2)xx200N`
`w_(m)=1/10xx4xx200=80N`