The reading of a spring balance when a block is suspended from it in air is 60 N. This reading is changed to 40 N when the block is submerged in water. The relative density of the block is:

Options

A. 3
B. 2
C. 6
D. `(3)/(2)`

Explanation

To find the relative density of the block based on the given information, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Weight of the Block in Air**:
- The reading of the spring balance when the block is suspended in air is given as 60 N. This represents the weight of the block (W).
- \( W = 60 \, \text{N} \)

2. **Identify the Weight of the Block in Water**:
- The reading of the spring balance when the block is submerged in water is given as 40 N. This is the apparent weight of the block in water (W').
- \( W' = 40 \, \text{N} \)

3. **Calculate the Buoyant Force**:
- The buoyant force (F_b) acting on the block can be calculated using the difference between the weight in air and the apparent weight in water.
- \( F_b = W - W' = 60 \, \text{N} - 40 \, \text{N} = 20 \, \text{N} \)

4. **Use the Buoyant Force to Relate to Volume**:
- The buoyant force can also be expressed using the formula:
\[ F_b = \rho_{water} \cdot V \cdot g \]
where \( \rho_{water} \) is the density of water (approximately \( 1000 \, \text{kg/m}^3 \)), \( V \) is the volume of the block, and \( g \) is the acceleration due to gravity.

5. **Express the Weight of the Block**:
- The weight of the block can be expressed as:
\[ W = \rho_{block} \cdot V \cdot g \]
where \( \rho_{block} \) is the density of the block.

6. **Set Up the Ratio for Relative Density**:
- The relative density (RD) of the block is defined as the ratio of the density of the block to the density of water:
\[ RD = \frac{\rho_{block}}{\rho_{water}} \]

7. **Relate the Two Equations**:
- From the equations for weight and buoyant force, we can relate the densities:
\[ F_b = W - W' \implies 20 \, \text{N} = \rho_{water} \cdot V \cdot g \]
\[ 60 \, \text{N} = \rho_{block} \cdot V \cdot g \]

8. **Eliminate Volume and Gravity**:
- By dividing the two equations, we eliminate \( V \) and \( g \):
\[ \frac{W}{F_b} = \frac{\rho_{block}}{\rho_{water}} \implies \frac{60 \, \text{N}}{20 \, \text{N}} = \frac{\rho_{block}}{\rho_{water}} \]

9. **Calculate the Relative Density**:
- Thus, we find:
\[ RD = \frac{60}{20} = 3 \]

### Final Answer:
The relative density of the block is **3**.

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