Question

See the image below for the question I attempted it but got a little jumbled up in my head and I want to make sure I got it right can anyone walk me through it step by step and show answer so I can compare?

Answer 1

Acceleration due to gravity on Europa is `1.3156` `m/(sec)^2`

A man weighing `100` `kg.` will weigh `13.416` `kg,`

Explanation:

Newton's law of gravitation states that force of gravity `F` between two objects of mass `m_1` and `m_2` at a distance of `r` from each other is given by

`F=G(m_1m_2)/r^2`

for a man on earth's surface, if his mass is `m` this force will be

`F=G(mM_E)/R_E^2`,

where `M_E` is mass of Earth and `R_E` is Earth's radius.

As this force is `mg_E`, we have `g_E=GM_E/R_E^2` and given Earth's mass and radius we have `g_E=9.806` `m/(sec)^2`. Here subscript `E` denotes Earth.

Similarly let subscipt `e` denote accelaration due to gravity `g_e` at Europa will be given by

`g_e=G(M_e)/R_e^2=6.67xx10^(-11)xx(4.8xx10^22)/(1.56xx10^6)^2`

= `(6.67xx4.8)/(1.56)^2xx10^((-11+22-12))`

= `13.156xx10^(-1)=1.3156` `m/(sec)^2`

i.e. Acceleration due to gravity on Europa is `1.3156` `m/(sec)^2`

A man weighing `100` `kg.` will weigh

`100xx1.3156/9.806=13.416` `kg,`