The gravitational pull on the moon is $\frac{1}{6}$ that of the earth. If a body weighs 6.0 N on the moon, what will be the weight on the earth?

Analysis

The question asks us to find the weight of an object on Earth, given its weight on the Moon and the relationship between the gravitational pull of the two bodies.

Concept

Weight ($W$) is the force of gravity acting on an object's mass ($m$). It is calculated using the formula:

where $g$ is the acceleration due to gravity.

Since the mass ($m$) of an object remains constant regardless of location, the ratio of weights on two different planets is directly proportional to the ratio of their gravitational accelerations:

Step-by-Step Solution

1. Identify the given information: • Weight on the Moon ($W_{moon}$) = 6.0 N • Gravitational pull on the Moon is $\frac{1}{6}$ that of the Earth, meaning: $$g_{moon} = \frac{1}{6} \times g_{earth}$$

2. Set up the relationship: From the concept above, we know: $$W_{moon} = \frac{1}{6} \times W_{earth}$$

3. Substitute the values: $$6.0\text{ N} = \frac{1}{6} \times W_{earth}$$

4. Solve for $W_{earth}$: Multiply both sides by 6: $$W_{earth} = 6.0\text{ N} \times 6$$ $$W_{earth} = 36.0\text{ N}$$

Conclusion

The weight of the body on Earth is 36.0 N.

Exam Tip

Always remember that mass is constant (it doesn't change whether you are on the Moon, Earth, or in space), but weight changes depending on the local gravity. If you are moving from a place with lower gravity (the Moon) to a place with higher gravity (the Earth), your weight must increase!