The weight of a person on any celestial body depends on the gravitational force exerted by the body on the person. With reference to the above fact and the relative gravitational pulls of the earth and the moon, what will the weight of a person be on the moon, if his weight on earth is 96 units?

Options

A. Approximately 16 units
B. Approximately 80 units
C. Approximately 96 units
D. Approximately 50 units

Answer

To find the weight of a person on the Moon given their weight on Earth, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between weight and gravitational pull**:
The weight of a person is determined by the gravitational force acting on them. This force is calculated using the formula:
\[ \text{Weight} = \text{Mass} \times \text{Gravitational Acceleration} (g) \]

2. **Identify the gravitational pull on Earth and the Moon**:
The gravitational pull on Earth (denoted as \( g_e \)) is approximately 9.8 m/s², while the gravitational pull on the Moon (denoted as \( g_m \)) is about 1/6th of that on Earth. Therefore:
\[ g_m = \frac{g_e}{6} \]

3. **Given the weight on Earth**:
The weight of the person on Earth is given as 96 units. This can be expressed as:
\[ \text{Weight on Earth} = \text{Mass} \times g_e = 96 \text{ units} \]

4. **Calculate the mass of the person**:
From the weight equation, we can find the mass of the person:
\[ \text{Mass} = \frac{\text{Weight on Earth}}{g_e} = \frac{96}{g_e} \]

5. **Calculate the weight on the Moon**:
Now, we can find the weight of the person on the Moon using the formula:
\[ \text{Weight on Moon} = \text{Mass} \times g_m \]
Substituting \( g_m = \frac{g_e}{6} \):
\[ \text{Weight on Moon} = \text{Mass} \times \frac{g_e}{6} \]

6. **Substituting the mass into the equation**:
We can substitute the mass we found earlier:
\[ \text{Weight on Moon} = \left(\frac{96}{g_e}\right) \times \frac{g_e}{6} \]
Simplifying this gives:
\[ \text{Weight on Moon} = \frac{96}{6} = 16 \text{ units} \]

### Final Answer:
The weight of the person on the Moon will be **16 units**.

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