Q.If the diameter of the pulley is 6 inches, length of pointer is 10 inches and distance travelled by pointer is 5 inches. Calculate the actual growth in length of plant.

Step 1. The arc auxanometer relates the pointer's swept distance to the plant's actual growth in length through the formula: actual growth in length = (distance travelled by the pointer x radius of the pulley) / length of the pointer - exactly the relationship the chapter's own worked example uses (radius 4 inches, pointer 20 inches, distance 10 inches, giving 2 inches of actual growth).

Step 2. This question gives the pulley figure as 6 inches, the pointer length as 10 inches, and the distance travelled by the pointer as 5 inches.

Step 3. Substituting these three values into the same formula in the same order as the worked example gives: actual growth = (5 x 6) / 10.

Step 4. Working this out: 5 x 6 = 30, and 30 / 10 = 3.

Step 5. So the actual growth in length of the plant works out to 3 inches, matching option (a); none of the other options (6, 12 or 30 inches) come from a straightforward application of the formula to these figures.

Substitute the given pulley, pointer-length and pointer-distance figures into the auxanometer formula actual growth = (distance x pulley figure) / pointer length, the same way the chapter's own worked example is solved.

• Halving the given pulley figure before using it, which does not match how the chapter's own worked example applies its pulley value in the formula.
• Multiplying or dividing the three numbers in the wrong order and landing on 6, 12 or 30 inches instead of 3.