Question: c. 0 1 2 3 4 mm 0 45 d 0 mm 0 45 40 top-right: A micrometer diagram with the sleeve scale marked 0 to 4 mm and the thimble scale marked 0 and 45, with the anvil and spindle shown at the left and right of the object. bottom-right: A micrometer diagram with the sleeve marked 0 and “mm”, and the thimble scale marked 0, 45, and 40, with the measuring faces on both sides.

1. **Problem Statement:** We are given two micrometer readings and need to find the measured lengths. 2. **Understanding Micrometer Readings:** A micrometer reading consists of two parts: - The sleeve scale reading (in mm), which shows the whole millimeters. - The thimble scale reading, which shows the fractional part of a millimeter. The thimble scale is usually divided into 50 or 100 divisions, each representing $0.01$ mm if 50 divisions. 3. **Formula for Micrometer Reading:** $$\text{Total Reading} = \text{Sleeve Reading} + \frac{\text{Thimble Reading}}{100}$$ Assuming the thimble scale divisions represent $0.01$ mm each. 4. **First Micrometer Reading (top-right):** - Sleeve reading: $4$ mm - Thimble reading: $45$ Calculate: $$\text{Reading}_1 = 4 + \frac{45}{100} = 4 + 0.45 = 4.45\ \text{mm}$$ 5. **Second Micrometer Reading (bottom-right):** - Sleeve reading: $0$ mm - Thimble reading: $45 + 40 = 85$ (assuming the thimble scale reading is $45$ and $40$ is an additional reading or a misinterpretation, but likely the thimble reading is $40$) Since the problem shows $0$ mm on sleeve and thimble scale marked $0, 45, 40$, we take the thimble reading as $40$. Calculate: $$\text{Reading}_2 = 0 + \frac{40}{100} = 0.40\ \text{mm}$$ 6. **Final Answers:** - First measurement: $4.45$ mm - Second measurement: $0.40$ mm These are the lengths measured by the micrometer in each case.