The reading of a spring balance when a mass is weighed on it in air is 40 gm. When the mass is immersed in water, its reading is 20 gm. The specific gravity of the mass is

Options

A. 3
B. 2
C. 1.5
D. 2.5

Answer

To find the specific gravity of the mass based on the given readings of the spring balance, we can follow these steps:

### Step 1: Identify the weights
- The weight of the mass in air (W_a) is given as 40 g.
- The weight of the mass when immersed in water (W_w) is given as 20 g.

### Step 2: Understand the concept of buoyancy
When the mass is immersed in water, it experiences an upward buoyant force, which reduces the reading on the spring balance. The difference between the weight in air and the weight in water gives us the buoyant force.

### Step 3: Calculate the buoyant force
The buoyant force (B) can be calculated as:
\[ B = W_a - W_w \]
Substituting the values:
\[ B = 40 \, \text{g} - 20 \, \text{g} = 20 \, \text{g} \]

### Step 4: Use the formula for specific gravity
The specific gravity (SG) of the mass is defined as the ratio of the weight of the mass in air to the loss of weight when submerged in water. The formula is:
\[ \text{SG} = \frac{W_a}{W_a - W_w} \]

### Step 5: Substitute the values into the formula
Substituting the known values:
\[ \text{SG} = \frac{40 \, \text{g}}{40 \, \text{g} - 20 \, \text{g}} \]
\[ \text{SG} = \frac{40 \, \text{g}}{20 \, \text{g}} \]

### Step 6: Simplify the expression
\[ \text{SG} = 2 \]

### Conclusion
The specific gravity of the mass is 2. This means the mass is twice as dense as water.

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