Question

A small particle elastically strikes a fixed smooth sphere of 4 cm radius with speed of 5m/s. The impact parameter for the collision is 2√3 cm. Calculate the angle of deflection of the particle.

Answer 1

Answer:

30' from horizontal then

Answer 2

Given:

Speed of the particle = 5m/s

Radius of sphere = 4cm

Impact parameter = 2√3 cm

To Find:

Angle of Deflection of the particle.

Solution:

• Impact parameter is defined as the perpendicular distance between the path of the particle and the line passing through the center of the sphere parallel to the path.
• Hence we can see from the diagram that the particle will travel in a direction perpendicular to the sphere at the point of collision.
• In the diagram ΔABC ,
• AB = Radius of sphere = 4cm
• AC = impact parameter = 2√3 cm

Therefore,

• sin x = AC/AB = 2√3/4 = √3/2
• x = 60 °

Now Then ,

• ∠PAQ = x = 60° ,
• Corresponding angles in parallel lines.

But if we observe the direction of particle,

• Its direction is along PA .
• Then the final direction is towards AQ.
• Therefore there is a deviation of 180° - 60° = 120°

The angle of deflection of the particle is 120°