**Answer:**

The center of mass of a system is the point at which the entire mass of the system can be considered to be concentrated. To find the center of mass of the system consisting of two spheres, we need to consider the masses and positions of the spheres.

**Finding the Center of Mass:**

To find the center of mass of the system, we can use the concept of weighted average. The center of mass of the system can be calculated using the formula:

**Center of Mass = (m1 * r1 + m2 * r2) / (m1 + m2)**

where m1 and m2 are the masses of the spheres, and r1 and r2 are their respective positions.

**Given Data:**
- Mass of sphere 1 (m1) = 10 kg
- Mass of sphere 2 (m2) = 5 kg
- Distance between the spheres (r) = 10 meters

**Calculating the Center of Mass:**

Let's calculate the center of mass of the system using the given data:

**Center of Mass = (10 kg * r1 + 5 kg * r2) / (10 kg + 5 kg)**

Since the spheres are situated on a long stick, we can assume that the stick is massless. Therefore, the mass of the stick is not considered in the calculation of the center of mass.

**Position of Sphere 1 (r1):**
Sphere 1 is located at one end of the stick, so its position can be considered as 0 meters.

**Position of Sphere 2 (r2):**
Sphere 2 is located at the other end of the stick, so its position can be considered as the distance between the spheres, which is 10 meters.

**Calculating the Center of Mass (continued):**

Using the given positions and masses, we can calculate:

**Center of Mass = (10 kg * 0 m + 5 kg * 10 m) / (10 kg + 5 kg)**

Simplifying further:

**Center of Mass = (0 kg * m + 50 kg * m) / 15 kg**

**Center of Mass = 50 kg * m / 15 kg**

**Center of Mass = 3.33 m**

Therefore, the center of mass of the system lies at a distance of 3.33 meters from Sphere 1 and 6.67 meters from Sphere 2.