**Projectile Motion on a Hollow Cone**

When a particle is projected from point P with velocity 5root3 m/s perpendicular to the surface of a hollow right angle cone, it collides normally at Q. Let's analyze the motion of the particle to find the velocity with which it collides at Q.

**Projectile Motion Analysis**

The initial velocity of the particle is perpendicular to the surface of the cone. Therefore, the motion of the particle can be separated into two components - horizontal and vertical.

The horizontal component of velocity remains constant throughout the motion as there is no acceleration in the horizontal direction. The vertical component of velocity changes due to the acceleration due to gravity.

The particle follows a parabolic path due to the vertical acceleration. The path of the particle intersects the surface of the cone at point Q.

**Velocity at Point Q**

At point Q, the velocity of the particle is perpendicular to the surface of the cone. Therefore, the horizontal component of velocity is zero, and the vertical component of velocity is the velocity with which the particle collides at Q.

The velocity with which the particle collides at Q can be found by using the conservation of energy principle. The potential energy of the particle at point P is converted into kinetic energy at point Q.

The potential energy of the particle at point P is given by mgh, where m is the mass of the particle, g is the acceleration due to gravity, and h is the height from point P to the ground level.

The kinetic energy of the particle at point Q is given by (1/2)mv^2, where v is the velocity with which the particle collides at Q.

Therefore, mgh = (1/2)mv^2

v = sqrt(2gh)

Substituting the values, v = sqrt(2*9.8*2) = 6.26 m/s

Therefore, the velocity with which the particle collides at Q is 6.26 m/s.