To understand why the stroke length will increase by 20% when the crank radius is increased from 10 cm to 12 cm, let's first define the terms involved in this mechanism.

The slider crank mechanism consists of three main parts:
1. Crank: It is the rotating arm that converts rotary motion into reciprocating motion.
2. Slider: It is the connecting rod that slides back and forth in a straight line.
3. Connecting rod: It connects the crank and the slider.

The stroke length is the distance traveled by the slider in a single motion cycle. It can be calculated as the difference between the maximum and minimum positions of the slider.

Now, let's analyze the effect of increasing the crank radius on the stroke length.

1. Relationship between crank radius and stroke length:
- The stroke length is directly proportional to the crank radius.
- When the crank radius increases, the stroke length also increases.

2. Calculation of stroke length:
- The stroke length can be calculated using the formula:
Stroke length = 2 * crank radius

3. Calculation for the initial crank radius of 10 cm:
- Stroke length = 2 * 10 cm = 20 cm

4. Calculation for the increased crank radius of 12 cm:
- Stroke length = 2 * 12 cm = 24 cm

5. Calculation of the percentage increase in stroke length:
- Percentage increase = (New value - Old value) / Old value * 100
- Percentage increase = (24 cm - 20 cm) / 20 cm * 100
- Percentage increase = 4 cm / 20 cm * 100
- Percentage increase = 0.2 * 100
- Percentage increase = 20%

Therefore, when the crank radius is increased from 10 cm to 12 cm, the stroke length increases by 20%. This means that the slider will travel 20% further in each motion cycle.