In a scenario where a thin metallic strip on a vernier caliper descends from the upper edge to the lower edge and makes constant contact with the surface of a beaker, the main scale displays a reading of 6.4 cm with a vernier constant of 1.1 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)
Convert the main scale reading to millimeters: 6.4 c m = 64 mm .
Calculate the vernier scale reading: 4 × 1.1 mm = 4.4 mm .
Add the main scale reading and the vernier scale reading to find the total reading: 64 mm + 4.4 mm = 68.4 mm .
State the precise depth of the beaker: 68.4 mm .
Explanation
Problem Analysis We are given the main scale reading of the vernier calliper as 6.4 cm, the vernier constant as 1.1 mm, and the fourth vernier scale division aligns with a main scale division. We need to determine the precise depth of the beaker, assuming there is no zero error.
Convert Units First, we need to convert the main scale reading from centimeters to millimeters to maintain consistent units. Since 1 cm = 10 mm, we have: 6.4 c m = 6.4 × 10 mm = 64 mm
Calculate Vernier Scale Reading Next, we calculate the vernier scale reading by multiplying the vernier constant by the division that aligns with a main scale division: V er ni er sc a l e re a d in g = 4 × 1.1 mm = 4.4 mm
Calculate Total Reading Now, we calculate the total reading by adding the main scale reading and the vernier scale reading: T o t a l re a d in g = M ain sc a l e re a d in g + V er ni er sc a l e re a d in g T o t a l re a d in g = 64 mm + 4.4 mm = 68.4 mm
Final Answer Therefore, the precise depth of the beaker is 68.4 mm.
Examples
Vernier callipers are used in various real-world applications, such as measuring the diameter of pipes, the thickness of materials, and the depth of holes. For example, a mechanic might use vernier callipers to accurately measure the diameter of a piston in an engine to ensure it fits properly. Similarly, a jeweller could use them to measure the thickness of a gemstone to ensure it meets the specifications for a particular setting. These precise measurements are crucial in engineering, manufacturing, and quality control to ensure accuracy and proper functionality.
The precise depth of the beaker, measured using a vernier caliper, is 68.4 mm. This is calculated by converting the main scale reading to millimeters and adding the vernier scale reading. Thus, the total depth is found by combining both of these measurements.
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