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This problem can be solved using the principle of moments (torque) to determine the distance from the center of gravity of the loaded trolley from the wheels. Let's break it down step by step:

### Known Values:
- Mass of the trolley and paving stone \(m = 18.5 \, \text{kg}\)
- Length of the trolley \(L = 97 \, \text{cm} = 0.97 \, \text{m}\)
- Force on the handle \(F = 50 \, \text{N}\)
- Gravitational acceleration \(g = 9.8 \, \text{m/s}^2\)
- The weight of the trolley and paving stone: \(W = mg = 18.5 \times 9.8 = 181.3 \, \text{N}\)

### Assumptions:
- The trolley is in rotational equilibrium, so the clockwise moments equal the anticlockwise moments.
- The force applied at the handle is a vertical force, acting perpendicular to the trolley.
  
### Setup the Moment Equation:
To apply the principle of moments, we consider the pivot point at the wheels (since the wheels are in contact with the ground). For rotational equilibrium, the moments about this point must balance:

\[
\text{Moment due to weight of trolley} = \text{Moment due to force on the handle}
\]

The distance from the center of gravity (which we will call \(x\)) is the unknown, and the distance from the handle to the pivot is the full length of the trolley, \(L = 0.97 \, \text{m}\).

So the equation is:
\[
W \times x = F \times L
\]
\[
181.3 \times x = 50 \times 0.97
\]
\[
181.3 \times x = 48.5
\]

### Solve for \(x\):
\[
x = \frac{48.5}{181.3} \approx 0.267 \, \text{m} = 26.7 \, \text{cm}
\]

### Final Answer:
The distance of the center of gravity of the loaded trolley from the wheels is approximately **26.7 cm**.

Would you like more details on any part of the solution, or do you have any questions?

Here are 5 related questions to expand on this topic:
1. How does the position of the center of gravity affect the stability of the trolley?
2. What happens to the force required on the handle if the mass of the load increases?
3. How would the solution change if the length of the trolley were longer?
4. Can you explain the difference between rotational and translational equilibrium?
5. How is torque affected by the angle at which the force is applied?

**Tip:** Always ensure that the forces and distances in moment calculations are perpendicular to each other to get accurate results.

A gardener used a trolley to move a paving stone. The mass of the trolley and paving stone is 18.5 kg, the length of the trolley is 97 cm, and the force applied to the handle is 50 N. Determine the distance of the center of gravity of the loaded trolley from the wheels.

Learn how to find the center of gravity for a trolley carrying a paving stone using the principle of moments and torque. The problem includes calculating forces and rotational equilibrium, suitable for physics students in Grades 10-12.

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