Two small carts of masses 8 kg and 12 kg are connected by a light...

Let the common acceleration of the two carts be $a$.

Considering both carts as a single system, the total mass is $M = 8 + 12 = 20\text{ kg}$.

The net external force acting on the system is $F = 50\text{ N}$.

Using Newton's second law, the acceleration of the system is:

$a = \dfrac{F}{M} = \dfrac{50}{20} = 2.5\text{ m/s}^2$

Let $T$ be the tension in the string connecting the two carts. Considering the free body diagram of the $8\text{ kg}$ cart, the only horizontal force acting on it is the tension $T$.

Applying Newton's second law to the $8\text{ kg}$ cart:

$T = m_1 a = 8 \times 2.5 = 20\text{ N}$

Answer: $20\text{ N}$