The moon's acceleration due to gravity is $\frac{1}{6}$ of the earth's value. The weight of a bowling ball on the moon would be

1. Analyze the Question

The question asks for the relationship between the weight of an object on the Moon compared to its weight on Earth, given that the Moon's acceleration due to gravity ($g_m$) is $\frac{1}{6}$ of the Earth's acceleration due to gravity ($g_e$).

2. Explain the Concept

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

Where:

• $m$ is the mass of the object (which remains constant regardless of location).
• $g$ is the acceleration due to gravity at that specific location.

Since mass ($m$) does not change when you move an object from Earth to the Moon, the weight is directly proportional to the acceleration due to gravity ($W \propto g$).

3. Show the Solution

• On Earth: The weight of the ball is $W_e = m \times g_e$
• On the Moon: The weight of the ball is $W_m = m \times g_m$

We are given that $g_m = \frac{1}{6} g_e$.

Substitute this into the weight formula for the Moon:

Since $(m \times g_e)$ is the weight on Earth ($W_e$), we have:

This confirms that the weight of the ball on the Moon is $\frac{1}{6}$ of its weight on Earth.

4. Identify the Answer

Comparing our result to the given options, the correct choice is B.

5. Exam Tip

Always remember the difference between Mass and Weight:

• Mass is the quantity of matter in a body and is constant everywhere (measured in kg).
• Weight is a force that changes depending on the gravitational field strength of the location (measured in Newtons).
• Strategy: If a question asks about "mass" on the moon, the answer is always "the same as on Earth." If it asks about "weight," apply the ratio of the gravitational fields.