The apparent weight of an object on the surface of the moon, if the mass of the object and liquid displaced are X and Y, respectively, is

Options

A. `(X-Y)/g`
B. `g/6(X-Y)`
C. 6g(X-Y)
D. `6/g(X-Y)`

Answer

To find the apparent weight of an object on the surface of the moon, given the mass of the object (X) and the mass of the liquid displaced (Y), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Buoyancy**:
When an object is immersed in a fluid, it experiences an upward force known as buoyancy. This force is equal to the weight of the fluid displaced by the object.

2. **Calculate the Buoyant Force**:
The buoyant force (B) can be calculated using the formula:
\[ B = g \times Y \]
where \( g \) is the acceleration due to gravity and \( Y \) is the mass of the liquid displaced.

3. **Determine the Weight of the Object**:
The weight (W) of the object in the fluid is given by:
\[ W = mg = g \times X \]
where \( X \) is the mass of the object.

4. **Calculate the Apparent Weight in the Fluid**:
The apparent weight of the object when submerged in the fluid is the actual weight minus the buoyant force:
\[ \text{Apparent Weight} = W - B = g \times X - g \times Y \]
Simplifying this gives:
\[ \text{Apparent Weight} = g(X - Y) \]

5. **Find the Weight on the Moon**:
The weight of an object on the moon is given by:
\[ \text{Weight on Moon} = \text{Apparent Weight} \times \frac{g}{6} \]
Since the acceleration due to gravity on the moon is approximately \( \frac{g}{6} \), we can substitute:
\[ \text{Weight on Moon} = g(X - Y) \times \frac{1}{6} \]
Thus, the apparent weight of the object on the moon becomes:
\[ \text{Apparent Weight on Moon} = \frac{g(X - Y)}{6} \]

### Final Answer:
The apparent weight of the object on the surface of the moon is:
\[ \frac{g(X - Y)}{6} \]