Question

On planet X, an object weighs 12.4 N. On planet B where the magnitude of the free-fall acceleration is 0.802 g (where g = 9.8 m/s² is the gravitational acceleration on Earth), the object weighs 29.1 N. The acceleration of gravity is 9.8 m/s². What is the mass of the object be on Earth? Answer in units of kg.​

Answer 1

Approximately
`3.7\; {\rm kg}`.

Step-by-step explanation:

The free-fall acceleration is equal to the gravitational field strength at that position. It is given that the free-fall acceleration on planet B is
`0.802\, (9.8\; {\rm m\cdot s^(-2)}) \approx 7.87\; {\rm m\cdot s^(-2)}`. The gravitational field strength on that planet would have the same value: approximately
`7.87\; {\rm m\cdot s^(-2)}`.

Note that
`1\; {\rm N} = 1\; {\rm kg\cdot m\cdot s^(-2)}`. Thus:

`\begin{aligned} 7.87\; {\rm m\cdot s^(-2)} &= 7.87\; {\rm m\cdot s^(-2)\cdot (kg\cdot kg^(-1))} \\ &= 7.87\; {\rm (kg \cdot m\cdot s^(-2))\cdot kg^(-1)} \\ &= 7.87\; {\rm N\cdot kg^(-1)} \end{aligned}`.

In other words, on this planet, the weight on every
`1\; {\rm kg}` of mass would be
`7.87\; {\rm N}`.

Divide the gravitational attraction (weight) on the object by the gravitational field strength to find the mass of this object:

`\begin{aligned}(\text{mass}) &= \frac{(\text{weight})}{(\text{gravitational field strength})} \\ &\approx \frac{29.1\; {\rm N}}{7.87\; {\rm N\cdot kg^(-1)}} \\ &\approx 3.7\; {\rm kg}\end{aligned}`.