A solid of density D is floating in a liquid of density d. If `upsilon` is the volume of solid submerged in the liquid and V is the total volume of the solid, then `upsilon//V` equal to

Options

A. `(d)/(D)`
B. `(D)/(d)`
C. `(D)/(D+d)`
D. `(D+d)/(D)`

Explanation

To solve the problem, we need to apply the principles of buoyancy and the relationship between the densities of the solid and the liquid.

### Step-by-Step Solution:

1. **Understand the Concept of Buoyancy**:
When a solid floats in a liquid, the weight of the solid is balanced by the buoyant force (upthrust) acting on it. This is known as Archimedes' principle.

2. **Write the Weight of the Solid**:
The weight of the solid can be expressed as:
\[ W = \text{Volume} \times \text{Density} \times g = V \times D \times g \]
where \( V \) is the total volume of the solid, \( D \) is the density of the solid, and \( g \) is the acceleration due to gravity.

3. **Write the Buoyant Force**:
The buoyant force (upthrust) acting on the solid is equal to the weight of the liquid displaced by the submerged part of the solid. This can be expressed as:
\[ F_b = \text{Volume submerged} \times \text{Density of liquid} \times g = \upsilon \times d \times g \]
where \( \upsilon \) is the volume of the solid submerged in the liquid and \( d \) is the density of the liquid.

4. **Set the Weight Equal to the Buoyant Force**:
Since the solid is floating, the weight of the solid is equal to the buoyant force:
\[ V \times D \times g = \upsilon \times d \times g \]
We can cancel \( g \) from both sides:
\[ V \times D = \upsilon \times d \]

5. **Rearranging the Equation**:
We can rearrange the equation to find the ratio of the submerged volume to the total volume:
\[ \frac{\upsilon}{V} = \frac{D}{d} \]

6. **Final Result**:
Therefore, the ratio of the volume of the solid submerged in the liquid to the total volume of the solid is given by:
\[ \frac{\upsilon}{V} = \frac{D}{d} \]