1. Given data

• Mass on table: $m_1 = 40\,\text{kg}$
• Hanging mass: $m_2 = 4\,\text{kg}$
• Coefficient of kinetic friction: $\mu_k = 0.02$
• Acceleration due to gravity: $g = 10\,\text{m s}^{-2}$

2. Friction on the 40 kg block

Since the block is sliding on the horizontal surface,

$f_k = \mu_k N = \mu_k m_1 g$

$f_k = 0.02 \times 40 \times 10 = 8\,\text{N}$

3. Driving force of the system

The hanging block pulls the system with weight

$m_2 g = 4 \times 10 = 40\,\text{N}$

Opposing this is friction on the 40 kg block:

$f_k = 8\,\text{N}$

So net external force on the two-block system is

$F_{\text{net}} = 40 - 8 = 32\,\text{N}$

4. Total mass of the system

$m_{\text{total}} = m_1 + m_2 = 40 + 4 = 44\,\text{kg}$

5. Acceleration of the system

Using Newton's second law for the complete system,

$a = \frac{F_{\text{net}}}{m_{\text{total}}} = \frac{32}{44} = \frac{8}{11}\,\text{m s}^{-2}$

6. Match with options

$\boxed{a = \frac{8}{11}\,\text{m s}^{-2}}$

So the correct option is D.