Question

A person that weighs 600 N on Earth travels to another planet with 5 times the mass and 5 times the radius of Earth. What is the weight of the person on this planet?

Answer 1

Given data

*The weight of the person is W = 600 N

*The other planet radius is R_p = 5 × R_e

*The other planet with mass is m_p = 5 × m_e

The formula for the acceleration due to gravity on the other planet is given as

`g=(Gm_p)/(R^2_p)`

Substitute the known values in the above expression as

`\begin{gathered} g_p=\frac{G(5* m_e)_{}}{(5R_e)^2} \\ =(Gm_e)/(5R^2_e) \\ =(g_e)/(5) \end{gathered}`

The mass of the person on the planet is calculated as

`\begin{gathered} m_p=(W)/(g_p) \\ =(600)/(g_p) \end{gathered}`

The weight of the person on the planet is calculated as

`\begin{gathered} W_p=m_pg_p \\ =(600)/(g_p)*(g_p)/(5) \\ =120\text{ N} \end{gathered}`