The weight of a person on the surface of the Earth is 490 N. Find his weight on the surface of Jupiter and the moon. Also, compare it with his weight on the Earth.
Mass of moon `= 7.3 xx 10^(22)` kg,
Mass of Jupiter `= 1.96 xx 10^(27)` kg,
Radius of moon `= 1.74 xx 10^(6)` m and radius of Jupiter `= 7 xx 10^(7)` m
`G = 6.67 xx 10^(-11) N m^(2) kg^(-2)` ltBrgt Given, `(1)/(1.742) = 0.33 "and ge" = 9.8 m s^(-2)`

Explanation

The mass of the person is `(W)/(g) = (490)/(9.8) = 50 kg`
Acceleration due to gravity on the moon, `g_(m)` is given by,
`g_(m) = (GM)/(R^(2))`
substituting the values,
`g_(m)=(6.67 xx 10^(-11) xx 7.3 xx 10^(22))/((1.74 xx 10^(6))^(2))=161 ms^(-2)`
weight on the moon `= mg = 50 xx 1.61 = 80.5 N` the ratio of weight on the moon to earth is `= (80.5)/(490) = 0.16`
Acceleration due to gravity on Jupiter is, `(g_(p))`
`g_(p) = (GM)/(R^(2))`
Substitution the values,
`g_(p) = (6.67 xx 10^(-11) xx 1.96 xx 10^(27))/((7 xx 10^(7))^(2))`
`= (6.67 xx 1.96 xx 10^(16))/(49 xx 10^(14)) = 26.68 ms^(-2)`
weight of person on Jupiter is ` = m xx g_(p) = 50 xx 26.68 = 1334 N`
ratio of weight on Jupiter to weight on earth is