Specific gravity has… dimensions in mass, ….. Dimensions in length and .. Dimensions in time.

Options

A. A) 0, 0, 0
B. B) 0, 1, 0
C. C) 1, 0, 0
D. D) 1, 1, 3

Answer

To solve the question regarding the dimensions of specific gravity, we can follow these steps:

### Step 1: Understand the Concept of Specific Gravity
Specific gravity is defined as the ratio of the density of a substance to the density of water (typically at 4 degrees Celsius). It is a dimensionless quantity.

### Step 2: Write the Formula for Density
The formula for density (ρ) is given by:
\[ \rho = \frac{m}{V} \]
where \(m\) is mass and \(V\) is volume.

### Step 3: Determine the Dimensions of Mass and Volume
- The dimensional formula for mass (m) is represented as \([M]\).
- The dimensional formula for volume (V) is given by \(L^3\), so the dimensional formula for volume is \([L^3]\).

### Step 4: Write the Dimensional Formula for Density
Using the formula for density:
\[ \rho = \frac{m}{V} = \frac{[M]}{[L^3]} = [M][L^{-3}] \]
Thus, the dimensional formula for density is:
\[ \rho = [M L^{-3}] \]

### Step 5: Write the Dimensional Formula for Specific Gravity
Since specific gravity is the ratio of the density of a substance to the density of water, we can express it as:
\[ \text{Specific Gravity} = \frac{\text{Density of Substance}}{\text{Density of Water}} = \frac{[M L^{-3}]}{[M L^{-3}]} \]
When we divide these two quantities, the mass and length dimensions cancel out:
\[ \text{Specific Gravity} = [M L^{-3}] / [M L^{-3}] = [M^0 L^0] = 1 \]
This means that specific gravity is dimensionless.

### Step 6: Conclusion on Dimensions
Since specific gravity is dimensionless, we can conclude:
- Dimensions in mass: \(0\)
- Dimensions in length: \(0\)
- Dimensions in time: \(0\)

Thus, the final answer is:
- Specific gravity has **0 dimensions in mass, 0 dimensions in length, and 0 dimensions in time**.

### Final Answer
Specific gravity has:
- Dimensions in mass: **0**
- Dimensions in length: **0**
- Dimensions in time: **0**