The terminal speed of a sphere of gold of density 22.5 `kg//m^(3)` is 40 cm/s in a viscous liquid of density 2.5 `kg//m^(3)` Find the terminal speed of a sphere of aluminium of density 15.5 `kg//m^(3)` of same size in same liquid.

Explanation

To find the terminal speed of a sphere of aluminum in the same viscous liquid, we can use the relationship between the terminal speeds of two spheres of different materials but the same size.

### Step-by-Step Solution:

1. **Identify the given values:**
- Density of gold, \( \rho_1 = 22.5 \, \text{kg/m}^3 \)
- Terminal speed of gold sphere, \( V_1 = 40 \, \text{cm/s} = 0.4 \, \text{m/s} \)
- Density of aluminum, \( \rho_2 = 15.5 \, \text{kg/m}^3 \)
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