**Given Information:**
- Mass of the block, m = 10 kg
- Acceleration of the block, a = 5 m/s^2
- When the force is doubled, acceleration becomes 18 m/s^2
- Acceleration due to gravity, g = 10 m/s^2

**Introduction:**
In this problem, we are given the mass of a block and its acceleration on a rough horizontal plane. We are also given the effect of doubling the force on the acceleration of the block. Our task is to determine the coefficient of friction between the block and the plane.

**Understanding the Problem:**
When a force is applied to the block, it experiences both the force and friction in the opposite direction. The frictional force can be determined using the equation:

Frictional force (Ff) = μ * Normal force (Fn)

Where:
- Frictional force (Ff) is the force opposing the motion of the block
- μ is the coefficient of friction
- Normal force (Fn) is the force exerted by the surface on the block perpendicular to the surface

**Determining the Coefficient of Friction:**
To find the coefficient of friction, we need to consider the following:

1. When the force is F and the acceleration is a:
- The net force on the block is given by F - Ff = m * a
- The normal force (Fn) is equal to the weight of the block, which is m * g

2. When the force is 2F and the acceleration is 18 m/s^2:
- The net force on the block is given by 2F - Ff = m * 18
- The normal force (Fn) is still equal to m * g

**Using the Equations:**
We can now use these equations to solve for the coefficient of friction:

1. When the force is F and the acceleration is a:
- F - μ * m * g = m * a

2. When the force is 2F and the acceleration is 18 m/s^2:
- 2F - μ * m * g = m * 18

**Simplifying the Equations:**
Let's rearrange the equations and express them in terms of the coefficient of friction:

1. F - μ * m * g = m * a
- F = m * a + μ * m * g
- F = m * (a + μ * g)

2. 2F - μ * m * g = m * 18
- 2F = m * 18 + μ * m * g
- 2F = m * (18 + μ * g)

**Comparing the Equations:**
Since the mass of the block (m) is the same in both equations, we can equate the expressions inside the brackets:

a + μ * g = 18 + μ * g

We can cancel out μ * g from both sides of the equation:

a = 18

Therefore, the acceleration is independent of the coefficient of friction. This implies that the coefficient of friction does not affect the acceleration of the block.

**Calculating the Coefficient of Friction:**
Now, we can substitute the given values into the equation:

5 = 18

Simplifying further:

μ * 10 * 10 = 5

μ =

1st eqn. F-f=ma
F=50+f
in 2nd eqn. 2F-f=ma
2F=180+f
equating 1&2 we get,
f=80
f=¶N ¶=coefficient of friction
N=mg
f=¶mg
¶=0.8