Introduction:
The problem states that a tunnel is dug along a chord of the Earth, at a perpendicular distance of R/2 from the Earth's center. The tunnel's wall is assumed to be frictionless. A particle is released from one end of the tunnel, and we need to draw graphs between the pressing force by the particle on the wall with x and the acceleration of the particle as it varies with x.

Explanation:
To understand the problem, let's break it down into steps and analyze each step in detail.

Step 1: Understanding the Setup
- The tunnel is dug along a chord of the Earth, which means it is a straight line connecting two points on the Earth's surface.
- The perpendicular distance of the tunnel from the Earth's center is R/2. This means that the tunnel is not at the Earth's equator but at a latitude where the distance from the center is R/2.
- The wall of the tunnel is assumed to be frictionless, which means there is no friction force acting on the particle as it moves along the tunnel.

Step 2: Analyzing the Particle's Motion
- When the particle is released from one end of the tunnel, it will start moving towards the other end.
- As the particle moves along the tunnel, its distance from the Earth's center will change, which we denote as x.
- The particle experiences a gravitational force towards the Earth's center, which is given by the equation F = (G * M * m) / r^2, where G is the gravitational constant, M is the mass of the Earth, m is the mass of the particle, and r is the distance between the particle and the Earth's center.

Step 3: Graphing the Pressing Force with x
- The pressing force by the particle on the wall of the tunnel can be calculated using the equation F_press = F * cos(theta), where F is the gravitational force and theta is the angle between the gravitational force and the tunnel's wall.
- Since the tunnel is perpendicular to the radius of the Earth at the point where the particle is located, the angle theta is 90 degrees. Therefore, cos(theta) = 0, and the pressing force is zero. As a result, the graph of pressing force vs. x will be a straight line at zero.

Step 4: Graphing the Acceleration with x
- The acceleration of the particle can be calculated using the equation a = F_net / m, where F_net is the net force acting on the particle.
- The net force acting on the particle is the gravitational force minus the pressing force, as there are no other forces acting on the particle.
- Since the pressing force is zero, the net force acting on the particle is equal to the gravitational force.
- Therefore, the acceleration of the particle is constant and equal to the gravitational acceleration, g = (G * M) / r^2.
- As the distance x from the Earth's center increases, the acceleration remains constant.
- Thus, the graph of acceleration vs. x will be a horizontal line at a constant value.

Conclusion:
In conclusion, the graph of pressing force by the particle on the wall of the tunnel vs. x will be a straight line at zero, as the pressing force is zero. The graph of acceleration of the