Gold is heavier than aluminium. If we put a 100 g biscult of gold in water taken in a measuring cylinder or we put a 100 g aluminium bar in the measuring cylinder, will the rise in level of water be same or different in the two cases ? Give reason.

Answer

To determine whether the rise in the level of water will be the same or different when a 100 g biscuit of gold and a 100 g aluminum bar are placed in a measuring cylinder filled with water, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Density**:
- Density is defined as mass per unit volume (Density = Mass/Volume).
- Gold is denser than aluminum. The density of gold is approximately 19.3 g/cm³, while the density of aluminum is about 2.7 g/cm³.

2. **Calculate the Volume of Each Material**:
- For gold:
- Given mass = 100 g
- Density of gold = 19.3 g/cm³
- Volume of gold = Mass/Density = 100 g / 19.3 g/cm³ ≈ 5.18 cm³.
- For aluminum:
- Given mass = 100 g
- Density of aluminum = 2.7 g/cm³
- Volume of aluminum = Mass/Density = 100 g / 2.7 g/cm³ ≈ 37.04 cm³.

3. **Determine the Rise in Water Level**:
- When an object is submerged in water, it displaces a volume of water equal to the volume of the object.
- Therefore, the rise in water level when the gold biscuit is submerged will be approximately 5.18 cm³.
- The rise in water level when the aluminum bar is submerged will be approximately 37.04 cm³.

4. **Compare the Two Volumes**:
- The volume displaced by the gold (5.18 cm³) is much less than that displaced by the aluminum (37.04 cm³).
- This indicates that the rise in water level will be different in the two cases.

5. **Conclusion**:
- The rise in the level of water will be different when a 100 g biscuit of gold and a 100 g aluminum bar are placed in the measuring cylinder. The rise will be less for gold compared to aluminum due to its higher density and lower volume.