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

Answer

a

Explanation

According to the law of gravitation the force of attraction acting on the body due due to earth is given by
`F = G(M_(e)m)/(R_(e)^(2))` …(1)
Also from newton's second law , we have
`mg = F` …(2)
`:. mgG=(M_(e)m)/(R_(e)^(2))`…(3)
`(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)R_(m)` their ratio
`Given R_(e) = 6400 R_(m) = 3200`
`(M_(e))/(M_(m)) = 10,w_(e) = 200 N`
`:. w_(m) = (1)/(10) ((6400)/(3200))^(2) xx 200`
`w_(m) = (1)/(10) xx 4 xx 200 = 80 N`