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The problem involves a rod and a disc in equilibrium, with forces acting at certain points. Here's the breakdown:

### Given:
- **Rod AB** of weight \( 2W \) and length \( 3a \), hinged to the horizontal plane at point \( A \). 
- A **disc** of weight \( W \) resting on the horizontal plane between the rod and the wall.
- The disc touches the rod at point \( P \) and the wall at point \( Q \).
- Angle \( BAC = 60^\circ \).
- The system is in equilibrium, in the vertical plane.

### Tasks:
1. **Part (a):** Find the magnitude of the reaction at \( B \), denoted as \( \frac{7\sqrt{3}}{8} W \).
2. **Part (b):** Find the magnitude of the reaction on \( AB \) at \( A \), in terms of \( kW \).

### Approach:

#### Part (a): 
We'll need to calculate the forces acting on the system and use equilibrium conditions. Since equilibrium is mentioned:
- **Vertical equilibrium:** The sum of all vertical forces must be zero.
- **Horizontal equilibrium:** The sum of all horizontal forces must be zero.
- **Moment equilibrium:** The sum of the moments about any point must be zero.

#### Part (b):
To solve for the reaction at \( A \), the vertical and horizontal components of forces acting at \( A \) must be determined.

Would you like a step-by-step solution for this problem? I can start with analyzing the forces, writing equilibrium equations, and solving for the unknowns.

Two parallel vertical smooth walls EF and CD meet a horizontal plane at E and C, respectively. A uniform smooth rod AB, of weight 2W and length 3a, is freely hinged to the horizontal plane at the point A. Between A and E, the rod AB rests against CD. A uniform smooth disc of weight W is in contact with the wall EF at the point P and with the rod at the point Q. It is given that angle BAC is 60 degrees and that the rod and disc are in equilibrium in the same vertical plane, which is perpendicular to both walls. Show that (a) the magnitude of the reaction at B is (7√3/8)W and (b) the magnitude of the reaction on AB at A is kW, giving the value of k correct to 3 significant figures.

Solve a statics problem involving a uniform rod AB and a disc in equilibrium. Learn how to calculate the reaction at point B and the reaction at the hinge point A using the principles of equilibrium of forces and moments. Suitable for university-level physics or engineering students.

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