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`

Answer

To find the relative density of the block, we can follow these steps:

### Step 1: Understand the Forces Acting on the Block
When the block is suspended in air, the reading on the spring balance (T) is equal to the weight of the block (W). When the block is submerged in water, the reading changes due to the buoyant force (FB) acting on the block.

### Step 2: Write the Equations
1. In air:
\[ T = W = 60 \, \text{N} \]

2. In water:
\[ T' = W - F_B \]
where \( T' = 40 \, \text{N} \).

### Step 3: Calculate the Buoyant Force
From the second equation, we can express the buoyant force:
\[ F_B = W - T' = 60 \, \text{N} - 40 \, \text{N} = 20 \, \text{N} \]

### Step 4: Relate Buoyant Force to Volume Displaced
The buoyant force can also be expressed as:
\[ F_B = \rho_{fluid} \cdot g \cdot V \]
where \( \rho_{fluid} \) is the density of water, \( g \) is the acceleration due to gravity, and \( V \) is the volume of the block.

### Step 5: Use the Definition of Relative Density
The relative density (specific gravity) of the block is given by:
\[ \text{Relative Density} = \frac{\text{Density of Block}}{\text{Density of Fluid}} \]
From Archimedes’ principle, we know that:
\[ F_B = \rho_{fluid} \cdot g \cdot V \]
Since the weight of the block (W) can also be expressed as:
\[ W = \text{Density of Block} \cdot g \cdot V \]

### Step 6: Set Up the Ratio
From the equations:
\[ F_B = 20 \, \text{N} = \rho_{fluid} \cdot g \cdot V \]
\[ W = 60 \, \text{N} = \text{Density of Block} \cdot g \cdot V \]

Dividing the weight of the block by the buoyant force gives:
\[ \frac{W}{F_B} = \frac{60 \, \text{N}}{20 \, \text{N}} = 3 \]

### Step 7: Conclusion
Thus, the relative density of the block is:
\[ \text{Relative Density} = 3 \]

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

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