# Which of these objects would have greater mass, object A that weighs 50N on earth or object B with a weight of 50N on the moon?

Jul 28, 2017

Object B (The object on the Moon)

#### Explanation:

We're asked to find which of two objects has a greater mass, given that they have the same weight on two different celestial bodies.

Recall Newton's second law, which states

$\sum \vec{F} = m \vec{a}$

We need to know the magnitude of the acceleration $g$ for each body. We know earth's is $9.81$ ${\text{m/s}}^{2}$, and the Moon's is $1.624$ ${\text{m/s}}^{2}$ (from Internet or any resource).

Earth:

We have

• $\sum F = 50$ $\text{N}$ (weight)

• $a = 9.81$ ${\text{m/s}}^{2}$

Thus,

m = (sumF)/a = color(red)(5.10 color(red)("g"

Moon:

We have

• $\sum F = 50$ $\text{N}$ (weight)

• $a = 1.624$ ${\text{m/s}}^{2}$

So

m = (sumF)/a = color(blue)(30.8 color(blue)("g"

Thus, object sfcolor(blue)("B" has the greater mass.

Jul 29, 2017

B

#### Explanation:

Intuitively, since gravity on the moon is less than that on Earth, it takes more mass on the moon to produce the same force.