Question

The magnitude of the acceleration due to gravity on the surface of planet A is twice as great as on the surface of planet B. What is the ratio of the weight of mass X on the surface of planet A to its weight on the surface of planet B?A) 1:2B) 2:1C) 1:4D) 4:1

Answer 1

Taking into account that

$\begin{gathered} g_A=2g_B \\ \text{Where } \\ g_A\Rightarrow\text{ gravity on the surface of the planet A} \\ g_B\Rightarrow\text{ gravity on the surface of the planet B} \end{gathered}$

And that the relationship between weight, mass and acceleration is

$w=m\cdot g$

So you have,

$\begin{gathered} w_A=m\cdot g_A \\ \text{ but you know that }g_A=2g_B,\text{ so you can replace} \\ w_A=m\cdot2g_B \\ w_A=2m\cdot g_B \\ w_A=2w_B \end{gathered}$

Therefore, the ratio of the weight of mass X on the surface of planet A to its weight on the surface of planet B is 1:2.