Determine the tension in the string as shown in the figure. The...

Let $T$ be the tension in the string and $a$ be the magnitude of acceleration of the blocks.

For the hanging block of mass $m_2 = 1 \text{ kg}$, the forces acting on it are the downward gravitational force $m_2g$ and the upward tension $T$. Assuming it accelerates downwards with acceleration $a$, its equation of motion is:
$m_2g - T = m_2a$
$10 - T = 1 \cdot a \quad \dots (1)$

For the block on the horizontal surface of mass $m_1 = 1 \text{ kg}$, the string is attached to its left side, passes around the left pulley, and then goes to the right pulley. When the hanging mass moves downwards, the string pulls the block to the left. The only horizontal force acting on this block is the tension $T$ directed to the left. Since the length of the string is constant, its acceleration is also $a$ to the left. Its equation of motion is:
$T = m_1a$
$T = 1 \cdot a \quad \dots (2)$

Substituting the value of $a$ from equation (2) into equation (1), we get:
$10 - T = T$
$2T = 10$
$T = 5 \text{ N}$

The tension in the string is $5 \text{ N}$.

Answer: $5 \text{ N}$