A hollow spherical object weighs 25 g in air. Its material density is ` 5 g//cm^(3)` . If it weights 15 g in water , then the volume (in ` cm^(3)` ) of the hollow space in it will be ________

Explanation

To solve the problem, we need to find the volume of the hollow space in a hollow spherical object given its weight in air, its weight in water, and the density of the material.

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Weight of the hollow spherical object in air (W_air) = 25 g
- Weight of the hollow spherical object in water (W_water) = 15 g
- Density of the material (ρ_material) = 5 g/cm³

2. **Calculate the Volume of the Material (V_m):**
- The volume of the material can be calculated using the formula:
\[ V_m = \frac{W_{\text{air}}}{\rho_{\text{material}}} \]
- Substituting the values:
\[ V_m = \frac{25 \text{ g}}{5 \text{ g/cm}^3} = 5 \text{ cm}^3 \]

3. **Calculate the Upthrust (Buoyant Force):**
- The upthrust (U) can be calculated using the difference in weight when submerged in water:
\[ U = W_{\text{air}} - W_{\text{water}} = 25 \text{ g} - 15 \text{ g} = 10 \text{ g} \]

4. **Relate Upthrust to Volume of Water Displaced:**
- The upthrust is equal to the weight of the water displaced, which can be expressed as:
\[ U = V_t \cdot \rho_{\text{water}} \]
- Since the density of water (ρ_water) is approximately 1 g/cm³, we can write:
\[ 10 \text{ g} = V_t \cdot 1 \text{ g/cm}^3 \]
- Therefore, the total volume (V_t) is:
\[ V_t = 10 \text{ cm}^3 \]

5. **Calculate the Volume of the Hollow Space (V_H):**
- The volume of the hollow space can be calculated as:
\[ V_H = V_t - V_m \]
- Substituting the values:
\[ V_H = 10 \text{ cm}^3 - 5 \text{ cm}^3 = 5 \text{ cm}^3 \]

### Final Answer:
The volume of the hollow space in the object is **5 cm³**.

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