An object weighs 60 N at the surface of earth. How much will it weigh at the surface of the moon ? `["Given" g_(m)=(1)/(6)g_(e)]`

Options

A. 1N
B. 10N
C. 6N
D. 360N

Answer

To find the weight of an object at the surface of the Moon, we can use the relationship between weight, mass, and acceleration due to gravity. The weight of an object is given by the formula:

\[ W = m \cdot g \]

Where:
- \( W \) is the weight of the object,
- \( m \) is the mass of the object,
- \( g \) is the acceleration due to gravity.

### Step-by-Step Solution:

1. **Identify the weight on Earth**:
The weight of the object at the surface of the Earth is given as 60 N.

2. **Use the relationship between weight and gravity**:
We know that the weight on Earth can be expressed as:
\[ W_e = m \cdot g_e \]
Where \( g_e \) is the acceleration due to gravity on Earth.

3. **Determine the mass of the object**:
Rearranging the equation gives us the mass:
\[ m = \frac{W_e}{g_e} \]
Since we don't need the actual value of \( g_e \) (approximately 9.8 m/s²), we can keep it as \( g_e \).

4. **Weight on the Moon**:
The weight of the object on the Moon can be expressed as:
\[ W_m = m \cdot g_m \]
Where \( g_m \) is the acceleration due to gravity on the Moon.

5. **Use the given relationship between \( g_m \) and \( g_e \)**:
We are given that:
\[ g_m = \frac{1}{6} g_e \]

6. **Substituting the mass into the weight equation for the Moon**:
Now substituting the expression for mass \( m \) into the weight equation for the Moon:
\[ W_m = \left(\frac{W_e}{g_e}\right) \cdot g_m \]

7. **Substituting \( g_m \)**:
Substitute \( g_m \) with \( \frac{1}{6} g_e \):
\[ W_m = \left(\frac{W_e}{g_e}\right) \cdot \left(\frac{1}{6} g_e\right) \]

8. **Simplifying the equation**:
The \( g_e \) terms cancel out:
\[ W_m = \frac{W_e}{6} \]

9. **Substituting the weight on Earth**:
Now substitute \( W_e = 60 \, \text{N} \):
\[ W_m = \frac{60 \, \text{N}}{6} \]

10. **Calculating the weight on the Moon**:
\[ W_m = 10 \, \text{N} \]

### Final Answer:
The weight of the object at the surface of the Moon is **10 N**.