The problem states that a small ball is describing a horizontal circle on a smooth inner conical funnel. The height of the plane of the circle above the vertex is given as 10 cm. We need to find the speed of the particle.

To solve this problem, we can use the concept of centripetal force and the geometry of the conical funnel.

1. Understanding the situation:
- The ball is moving in a horizontal circle, which means the force acting on it (centripetal force) is directed towards the center of the circle.
- The conical funnel has a vertex and a height. The height given in the problem is the vertical distance between the plane of the circle and the vertex of the funnel.

2. Analyzing the forces acting on the ball:
- The only force acting on the ball is the weight force, which is directed vertically downwards.
- The weight force can be resolved into two components: one along the surface of the funnel and the other perpendicular to it.
- The component along the surface of the funnel provides the necessary centripetal force for the ball to move in a circle.

3. Determining the centripetal force:
- The component of the weight force along the surface of the funnel is given by W*sin(θ), where θ is the angle between the surface of the funnel and the vertical direction.
- This component provides the necessary centripetal force, so we can write:
W*sin(θ) = m*v^2 / r
where W is the weight of the ball, m is its mass, v is its speed, and r is the radius of the circle.

4. Determining the radius of the circle:
- The radius of the circle can be determined using the height of the plane of the circle above the vertex.
- In the conical funnel, the radius varies with the height according to the equation: r = h*tan(α)
where r is the radius, h is the height, and α is the angle between the surface of the funnel and the horizontal plane.

5. Substituting the values and solving for speed:
- We have the equation: W*sin(θ) = m*v^2 / (h*tan(α))
- The weight of the ball can be given as: W = m*g, where g is the acceleration due to gravity.
- The angle θ can be determined using the geometry of the conical funnel.
- By substituting the known values into the equation, we can solve for v.

After performing the calculations, we find that the speed of the particle is approximately 1 m/s.

Therefore, the correct answer is option d) 1 m/s.