1. **State the problem:** A ball of mass 0.5 kg falls freely from a height of 180 cm (which is 1.8 m) under gravity $g = 10$ m/s². We need to find the momentum of the ball when it reaches the ground. 2. **Calculate the velocity of the ball just before hitting the ground:** Using the equation for free fall velocity: $$v = \sqrt{2gh}$$ where $h = 1.8$ m and $g = 10$ m/s². 3. Substitute the values: $$v = \sqrt{2 \times 10 \times 1.8} = \sqrt{36} = 6 \text{ m/s}$$ 4. **Calculate the momentum:** Momentum $p$ is given by: $$p = mv$$ where $m = 0.5$ kg and $v = 6$ m/s. 5. Substitute the values: $$p = 0.5 \times 6 = 3 \text{ kg.m/s}$$ 6. **Answer:** The momentum of the ball when it reaches the ground is $3$ kg.m/s. Therefore, the correct choice is (a) 3 kg.m/s.