A spring balance shows 100 gf reading when a metallic sphere is suspended from its hook. When the completely immersed in water, the reading shown by the balance is 75gf. The relative density of the material of the sphere is

Options

A. 1
B. 2
C. 3
D. 4

Answer

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

### Step 1: Understand the readings on the spring balance
When the metallic sphere is suspended in air, the spring balance reads 100 gf (grams-force). This indicates the weight of the sphere in air.

### Step 2: Understand the reading when the sphere is immersed in water
When the sphere is completely immersed in water, the spring balance reads 75 gf. This indicates the apparent weight of the sphere when submerged.

### Step 3: Calculate the loss of weight when submerged
The loss of weight when the sphere is submerged in water can be calculated as follows:
\[ \text{Loss of weight} = \text{Weight in air} - \text{Apparent weight in water} \]
\[ \text{Loss of weight} = 100 \, \text{gf} - 75 \, \text{gf} = 25 \, \text{gf} \]

### Step 4: Relate the loss of weight to the weight of water displaced
According to Archimedes' principle, the loss of weight of the body when submerged is equal to the weight of the water displaced. Therefore, the weight of the water displaced is:
\[ \text{Weight of water displaced} = 25 \, \text{gf} \]

### Step 5: Calculate the relative density
The relative density (RD) of the material of the sphere is given by the formula:
\[ \text{Relative Density} = \frac{\text{Weight of solid in air}}{\text{Weight of water displaced}} \]
Substituting the values we have:
\[ \text{Relative Density} = \frac{100 \, \text{gf}}{25 \, \text{gf}} = 4 \]

### Conclusion
The relative density of the material of the sphere is 4.

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