Question

A planet is discovered that has twice the mass of Earth but the same gravitational acceleration. If you weigh 700 N on Earth, on the new planet you would weigh ____.

Multiple choice question.

A)
350 N


B)
700 N


C)
1,400 N


D)
2,800 N

Answer 1

To determine your weight on the new planet, we can use the concept of gravitational force. Weight (W) is calculated by the formula:

\[ W = m \cdot g \]

where:
- \( m \) is the mass of the object,
- \( g \) is the gravitational acceleration.

You weigh 700 N on Earth, and Earth has a gravitational acceleration of approximately \( 9.81 \, \text{m/s}^2 \). We can find your mass as follows:

\[
700 \, \text{N} = m \cdot 9.81 \, \text{m/s}^2 \implies m = \frac{700 \, \text{N}}{9.81 \, \text{m/s}^2} \approx 71.2 \, \text{kg}
\]

Now, if the new planet has twice the mass of Earth but the same gravitational acceleration, the gravitational acceleration \( g \) on this new planet would still remain \( 9.81 \, \text{m/s}^2 \) (as stated in the problem).

Thus, your weight on the new planet would be:

\[
W_{\text{new planet}} = m \cdot g = 71.2 \, \text{kg} \cdot 9.81 \, \text{m/s}^2 \approx 700 \, \text{N}
\]

Since the gravitational acceleration is the same, your weight remains the same.

Therefore, the correct answer is:

**B) 700 N**