In a scenario where a thin metallic strip on a vernier calliper descends from the upper edge to the lower edge and makes contact with the surface of a beaker, the main scale displays a reading of 6.4 $m$ with a vernier constant of 0.1 mm, and the fourth vernier scale division aligns precisely with a main scale division. Determine the precise depth of the beaker, assuming there is no zero error.
Answer (2)
The precise depth of the beaker is 6400.4 mm, calculated by adding the converted main scale reading of 6400 mm to the vernier scale reading of 0.4 mm. This approach ensures accuracy by using the measurements provided by the vernier caliper.
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Convert the main scale reading to millimeters: 6.4 m = 6400 mm .
Calculate the vernier scale reading: 4 × 0.1 mm = 0.4 mm .
Add the main scale reading and the vernier scale reading: 6400 mm + 0.4 mm = 6400.4 mm .
State the final answer: The precise depth of the beaker is 6400.4 mm .
Explanation
Problem Analysis We are given the main scale reading as 6.4 m, the vernier constant as 0.1 mm, and the 4th vernier scale division aligns with a main scale division. We need to find the precise depth of the beaker.
Convert Units First, let's convert the main scale reading from meters to millimeters. Since 1 m = 1000 mm, we have: 6.4 m = 6.4 × 1000 mm = 6400 mm
Calculate Vernier Reading Next, we calculate the vernier scale reading. The vernier constant is 0.1 mm, and the 4th division aligns, so the vernier scale reading is: 4 × 0.1 mm = 0.4 mm
Calculate Total Reading Now, we add the main scale reading and the vernier scale reading to find the total reading, which represents the depth of the beaker: 6400 mm + 0.4 mm = 6400.4 mm
Final Answer Therefore, the precise depth of the beaker is 6400.4 mm.
Examples
Vernier calipers are used in various real-world applications, such as measuring the internal and external diameters of pipes, the depth of holes, and the thickness of materials in manufacturing, engineering, and scientific research. For example, a machinist might use vernier calipers to precisely measure the dimensions of a component to ensure it meets the required specifications. Similarly, a scientist might use them to measure the dimensions of a sample in a laboratory experiment.
