To solve this problem, we need to consider the equilibrium of the beam. Let's assume that the beam has a length L and is carrying a uniformly distributed load with intensity w.

We can start by calculating the reaction forces at the two supports. Since the load is uniformly distributed, the total load on the beam is given by the product of the load intensity w and the length L:

Total load = w * L

Since the load is uniformly distributed, the load per unit length is given by:

Load per unit length = w

Now, let's consider the equilibrium of the beam. At the supports, we have two unknown reaction forces: R1 at support 1 and R2 at support 2.

The sum of the vertical forces acting on the beam must be zero, so we have:

R1 + R2 = Total load

Now, let's consider the moments about support 1. The moment of the total load about support 1 is zero, since the load is uniformly distributed. Therefore, we only need to consider the moment of the reaction force R2 about support 1.

The moment of R2 about support 1 is given by the product of the distance between support 1 and support 2 (L) and the reaction force R2:

Moment of R2 about support 1 = L * R2

Since the beam is in equilibrium, the sum of the moments about support 1 must also be zero. Therefore, we have:

L * R2 = 0

Since R2 cannot be zero (otherwise, the beam would not be supported), we can conclude that L must be zero. This means that the reaction force R2 must be zero, and the entire load is supported by support 1.

To summarize:

- The reaction force at support 1 is equal to the total load (R1 = Total load)
- The reaction force at support 2 is zero (R2 = 0)

Therefore, the beam carrying a uniformly distributed load rests only on support 1.