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### Problem Overview:
1. There are two vertical smooth walls, \( EF \) and \( CD \), that meet a horizontal plane at points \( E \) and \( C \), respectively. A uniform smooth rod \( AB \), of weight \( 2W \) and length \( 3a \), is hinged to the horizontal plane at \( A \). The rod is in contact with the wall \( EF \) at point \( B \).
2. A uniform smooth disc of weight \( W \) and radius \( a \) rests against both the wall \( EF \) at point \( P \) and the rod \( AB \) at point \( Q \). 
3. The given angle \( BAC \) is \( 60^\circ \), and the rod and the disc are in equilibrium in the same vertical plane.

### Tasks:
- **(a)** Calculate the magnitude of the reaction at \( B \) as \( \frac{7}{3}W \).
- **(b)** Find the magnitude of the reaction at \( P \) in terms of \( W \).
- **(c)** Find the magnitude of the reaction at \( A \), giving the value of \( k \) to 3 significant figures.

### Solving the Problem:

We will use the equilibrium conditions of forces and moments (torques) to solve this problem.

#### Part (a) - Reaction at \( B \):
This involves calculating the forces acting on the rod \( AB \) and using the principle of equilibrium:
1. The total force on the rod includes:
   - Its own weight, \( 2W \), acting at the center of the rod.
   - The reaction forces at \( A \) and \( B \).
   - The force from the disc on the rod at point \( Q \).

2. The vertical and horizontal components of the forces must balance. In addition, the moments about any point (commonly chosen as \( A \) for simplicity) must sum to zero.

We'll analyze these in more detail.

#### Part (b) - Reaction at \( P \):
This part focuses on the disc, which is in equilibrium under the action of:
1. The vertical force due to its weight, \( W \).
2. The horizontal reaction forces from the rod at point \( Q \) and the wall at point \( P \).

By considering the forces and moments acting on the disc, we can solve for the reaction at \( P \).

#### Part (c) - Reaction at \( A \):
In this part, we need to find the magnitude of the reaction at \( A \) in terms of \( W \), after solving for all the forces and balancing the equations of motion.

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Would you like to proceed with the detailed calculations for each part?

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 E and C. The end B 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° and that AQ = a (see diagram). The rod and the 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 7W/3, (b) the magnitude of the reaction at P is 7W/3, and (c) find, in the form kW, the magnitude of the reaction on AB at A, giving the value of k correct to 3 significant figures.

Explore the equilibrium conditions of a rod and disc in a statics problem. This problem involves calculating reaction forces at various points using equilibrium equations and trigonometry. Suitable for advanced high school and early undergraduate students.

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