Introduction:
In this problem, we are given the mass of a particle, its radius, and angular velocity. We need to find the change in linear velocity when the particle completes half of a revolution.

Given:
- Mass of the particle = 5g (0.005 kg)
- Radius of the circle = 0.5m
- Angular velocity = 6 rad/s

Formula:
The linear velocity of a particle moving in a circle can be calculated using the formula:
v = rω
where,
v is the linear velocity,
r is the radius of the circle, and
ω (omega) is the angular velocity.

Calculation:
1. Convert the mass from grams to kilograms:
Mass = 5g = 0.005 kg

2. Calculate the linear velocity using the given angular velocity:
v = rω
= 0.5m × 6 rad/s
= 3m/s

Change in Linear Velocity:
To find the change in linear velocity when the particle completes half of a revolution, we need to calculate the linear velocity at the starting and ending points of the half-revolution. The change in linear velocity will be the difference between these two velocities.

Linear Velocity at the Starting Point:
At the starting point of the half-revolution, the linear velocity is given by:
v1 = rω
= 0.5m × 6 rad/s
= 3m/s

Linear Velocity at the Ending Point:
At the ending point of the half-revolution, the angular displacement is π radians (180 degrees) as half of a revolution is completed. Using this angular displacement, we can calculate the linear velocity at the ending point:
v2 = rω
= 0.5m × 6 rad/s
= 3m/s

Change in Linear Velocity:
The change in linear velocity is given by the difference between the linear velocities at the starting and ending points:
Δv = v2 - v1
= 3m/s - 3m/s
= 0m/s

Conclusion:
The change in linear velocity when the particle completes half of a revolution is 0 m/s. This means that the linear velocity remains constant throughout the half-revolution.