1. Use equation of continuity for incompressible flow:

$A_1 v_1 = A_2 v_2$

where:

• $A_1 = \pi r_1^2$
• $A_2 = \pi r_2^2$
• $v_1 = 2\,\text{m/s}$

2. Given radii:

$r_1 = 2\,\text{cm}, \qquad r_2 = 1\,\text{cm}$

So,

$A_1 = \pi (2)^2 = 4\pi$ $A_2 = \pi (1)^2 = \pi$

3. Substitute into continuity equation:

$A_1 v_1 = A_2 v_2$

$4\pi \cdot 2 = \pi \cdot v_2$

$8\pi = \pi v_2$

$v_2 = 8\,\text{m/s}$

4. Therefore, the velocity of water at point (2) is:

$\boxed{8\,\text{m/s}}$

5. Check options:

• A: $4$ m/s ❌
• B: $6$ m/s ❌
• C: $2$ m/s ❌
• D: $8$ m/s ✅

Hence, the correct option is D.