A student uses a spring balance of range 500 g wt. He records the weight of a small iron cube of mass 100 g in air, in tap water and in a concentrated solution of common salt in water. His three readings taken in the given order are `W_(1), W_(2)` and `W_(3)`. His measurements could be

Options

A. `W_(1)=W_(2)=W_(3)`
B. `W_(1) gt W_(2) gt W_(3)`
C. `W_(1) lt W_(2) lt W_(3)`
D. `W_(1) lt W_(2) gt W_(3)`

Answer

To solve the problem, we need to analyze the weight readings of the iron cube in three different scenarios: in air, in tap water, and in a concentrated salt solution.

### Step-by-step Solution:

1. **Weight in Air (W1)**:
- The weight of the iron cube in air is simply its mass multiplied by the acceleration due to gravity.
- Given that the mass of the iron cube is 100 g, we have:
\[ W_1 = 100 \text{ g} \]

2. **Weight in Tap Water (W2)**:
- When the iron cube is submerged in tap water, it experiences a buoyant force equal to the weight of the water displaced by the cube.
- The weight of the cube in water can be calculated using the formula:
\[ W_2 = W_1 - \text{Weight of water displaced} \]
- The weight of water displaced can be calculated using the formula:
\[ \text{Weight of water displaced} = \rho_{water} \cdot V \cdot g \]
- Since the density of water (\(\rho_{water}\)) is approximately 1 g/cm³, and the volume \(V\) of the cube can be calculated from its mass (100 g), we can find that:
\[ V = \frac{100 \text{ g}}{\rho_{iron}} \quad (\text{Assuming density of iron is greater than water}) \]
- Thus, the weight in water will be less than the weight in air:
\[ W_2 < W_1 \]

3. **Weight in Concentrated Salt Solution (W3)**:
- In a concentrated salt solution, the density of the solution is greater than that of water. Therefore, the buoyant force acting on the cube will be greater than in tap water.
- The weight of the cube in the concentrated salt solution can be calculated similarly:
\[ W_3 = W_1 - \text{Weight of salt solution displaced} \]
- Since the density of the salt solution (\(\rho_{salt}\)) is greater than that of water, the weight of the cube in the salt solution will be less than in water:
\[ W_3 < W_2 \]

4. **Conclusion**:
- From the analysis, we can conclude the order of weights:
\[ W_1 > W_2 > W_3 \]
- Therefore, the readings taken by the student can be summarized as:
\[ W_1 = 100 \text{ g}, \quad W_2 < 100 \text{ g}, \quad W_3 < W_2 \]