Question

A space probe sent to Mars has a weight of 10,000 N on Earth (g = 10). What is its mass?

Answer 1

`1,\!000\; {\rm kg}`.

Step-by-step explanation:

The "
`g`" given in the question likely refers to the strength of the gravitational field. The standard unit of
`g` is
`{\rm m \cdot s^(-2)}`, same as the standard unit of acceleration. However, since
`1\; {\rm N} = 1\; {\rm kg \cdot m \cdot s^(-2)`, the standard unit of
`g` is equivalent to
`{\rm N \cdot kg^(-1)}`.

For instance, the gravitational strength on the surface of the earth is approximately
`g = 10\; {\rm N \cdot kg^(-1)}`. However, the question did not specify the unit of this value.

If the mass of an object is
`m`, the weight of that object would be
`(\text{weight}) = m\, g` when the gravitational field strength around that object is
`g`. It is given that for the object in this question,
`m\, g = (\text{weight}) = 10,\!000\; {\rm N}` when
`g = 10\; {\rm N \cdot kg^(-1)}`. Therefore, the mass
`m\!` of this object would be:

`\begin{aligned}m &= \frac{(\text{weight})}{g} \\ &= \frac{10,\!000\; {\rm N}}{10\; {\rm N \cdot kg^(-1)}} \\ &= 1,\! 000\; {\rm kg}\end{aligned}`.