An astronaut weighs 600 N on Earth. During a moon mission, she performs an experiment to measure her weight on the moon. Which value is closest to her expected weight on the moon, and why?
100 N, because the Moon's gravity is about one-sixth of Earth's.
To solve this question, we need to understand the effect of gravitational force on weight, which is a product of mass and gravitational acceleration. The formula for weight (\(W\)) is:
\(W = mg\)
where:
- \(m\) is the mass of the object (in kilograms).
- \(g\) is the acceleration due to gravity (in meters per second squared).
On Earth, the gravitational acceleration is approximately \(9.8 \, m/s^2\). On the Moon, however, it is about one-sixth of Earth's gravity, which is approximately \(1.63 \, m/s^2\).
Given that the astronaut weighs 600 N on Earth, we can find her weight on the Moon using the ratio of the gravitational forces. Since the Moon's gravity is about one-sixth of Earth's:
\(\text{Weight on the Moon} = \frac{1}{6} \times \text{Weight on Earth}\)
Substituting the given weight on Earth:
\(\text{Weight on the Moon} = \frac{1}{6} \times 600 \, \text{N} = 100 \, \text{N}\)
Therefore, the closest value to her expected weight on the Moon is 100 N. The option "100 N, because the Moon's gravity is about one-sixth of Earth's" is correct.
Let's analyze the other options to understand why they are incorrect:
- 200 N, because the Moon's gravity is about one-third of Earth's: Incorrect, as the Moon's gravity is approximately one-sixth, not one-third, of Earth's gravity.
- 600 N, because a person's weight remains unchanged on the Moon: Incorrect, because weight depends on local gravitational force, which is different on the Moon.
- 300 N, because the Moon's gravity is about one-half of Earth's: Incorrect, as the Moon's gravity is about one-sixth of Earth's.
Important Questions from Gravitation
Which one of the following statement is true for the relation, \(F= \frac{{G{m_1}{m_2}}}{{{r^2}}}\) ?
(All symbols have their usual meanings)Suppose there are two planets, 1 and 2, having the same density but their radii are R 1and R 2respectively, where R 1> R 2. The accelerations due to gravity on the surface of these planets are related as
LIGO stands for
If radius of the earth were to shrink by 1%, its mass remains the same, g would decrease by nearly
The radius of the Moon is about one-fourth that of the Earth and acceleration due to gravity on the moon is about one-sixth that on the earth. From this, we can conclude that the ratio of the mass of earth to the mass of the moon is about
