Introduction:
In this scenario, we have two bodies of masses m1 and m2 connected by a light string passing over a frictionless and massless pulley. The pulley is moving with uniform acceleration g/2. We need to determine the tension in the string.

Analysis:
To find the tension in the string, we can consider the forces acting on each body separately.

Body 1:
Let's consider body 1 with mass m1. The forces acting on this body are:
- The weight force (mg1) acting downwards.
- The tension force (T) acting upwards.

Since the pulley is moving with uniform acceleration g/2, the net force acting on body 1 will be the difference between the tension force and the weight force:

Net force on body 1 = T - mg1

According to Newton's second law, the net force is given by:

Net force on body 1 = m1 * acceleration

Body 2:
Now let's consider body 2 with mass m2. The forces acting on this body are:
- The weight force (mg2) acting downwards.
- The tension force (T) acting downwards.

The net force acting on body 2 will be the sum of the tension force and the weight force:

Net force on body 2 = T + mg2

According to Newton's second law, the net force is given by:

Net force on body 2 = m2 * acceleration

Tension in the string:
Since the tension force in the string is the same for both bodies, we can equate the expressions for the net forces on body 1 and body 2:

T - mg1 = m1 * acceleration (Equation 1)
T + mg2 = m2 * acceleration (Equation 2)

Adding Equation 1 and Equation 2, we get:

2T = (m1 + m2) * acceleration

Dividing both sides by 2, we find:

T = (m1 + m2) * acceleration / 2

Substituting the given acceleration value (g/2), we have:

T = (m1 + m2) * (g/2) / 2

Simplifying further:

T = (m1 + m2) * g / 4

Conclusion:
The tension in the string connecting the two bodies will be (m1 + m2) * g / 4.

T=(m1+m2)/2