How much would a W kg man weigh on the moon in terms of gravitational units ?

Options

A. `(W)/(6)` kg wt
B. 6 W kg wt
C. W kg wt
D. zero

Explanation

To find out how much a W kg man would weigh on the moon in terms of gravitational units, we can follow these steps:

### Step 1: Understand Weight on Earth
The weight of an object on Earth is given by the formula:
\[ W = m \cdot g \]
where:
- \( W \) is the weight in newtons (N),
- \( m \) is the mass in kilograms (kg),
- \( g \) is the acceleration due to gravity on Earth, approximately \( 9.8 \, \text{m/s}^2 \).

### Step 2: Weight of the Man on Earth
Given that the man has a weight of \( W \) kg on Earth, we can express his weight in terms of mass:
\[ W = m \cdot g \]
This implies that the mass \( m \) can be expressed as:
\[ m = \frac{W}{g} \]

### Step 3: Understand Weight on the Moon
On the moon, the acceleration due to gravity is much less than on Earth. The value of gravity on the moon \( g' \) is approximately:
\[ g' = \frac{g}{6} \]
This means that the weight of the man on the moon \( W' \) can be calculated using the same mass but with the moon's gravity:
\[ W' = m \cdot g' \]

### Step 4: Substitute the Mass
Substituting the expression for mass \( m \) into the weight formula for the moon:
\[ W' = \left(\frac{W}{g}\right) \cdot g' \]
Now substituting \( g' = \frac{g}{6} \):
\[ W' = \left(\frac{W}{g}\right) \cdot \left(\frac{g}{6}\right) \]

### Step 5: Simplify the Expression
Now simplify the expression:
\[ W' = \frac{W}{g} \cdot \frac{g}{6} = \frac{W}{6} \]

### Conclusion
Thus, the weight of a W kg man on the moon in terms of gravitational units is:
\[ W' = \frac{W}{6} \, \text{kg weight} \]