In a scenario where a thin metallic strip extends 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 cm with a vernier constant of 0.1 mm, and the fourth vernier scale division aligns precisely with a main scale division. Determine the depth of the beaker, assuming there is no zero error.
Answer (2)
To find the depth of the beaker, first, convert the main scale reading of 6.4 cm to 64 mm. Next, add the vernier scale reading of 0.4 mm to get a total of 64.4 mm, which is then converted back to centimeters, resulting in a depth of 6.44 cm.
;
Convert the main scale reading to millimeters: 6.4 cm = 64 mm .
Calculate the vernier scale reading: 0.1 mm × 4 = 0.4 mm .
Add the main scale and vernier scale readings: 64 mm + 0.4 mm = 64.4 mm .
Convert the total reading back to centimeters: 64.4 mm = 6.44 cm .
The depth of the beaker is 6.44 cm .
Explanation
Problem Analysis Let's break down this problem step by step to find the depth of the beaker! We're given a main scale reading, a vernier constant, and the vernier scale division that aligns with the main scale. Our goal is to combine these pieces of information to get the most accurate depth measurement possible.
Convert to Millimeters First, we need to convert all our measurements to the same unit. Since the vernier constant is given in millimeters (mm), let's convert the main scale reading from centimeters (cm) to millimeters (mm). We know that 1 cm = 10 mm, so:
Main scale reading in mm = 6.4 cm * 10 mm/cm = 64 mm
Calculate Vernier Scale Reading Next, we need to calculate the vernier scale reading. This is found by multiplying the vernier constant by the division number on the vernier scale that aligns perfectly with a division on the main scale. In this case, the 4th vernier scale division aligns, and the vernier constant is 0.1 mm. So:
Vernier scale reading = Vernier constant * Division number Vernier scale reading = 0.1 mm * 4 = 0.4 mm
Add Main and Vernier Readings Now, we add the main scale reading and the vernier scale reading to get the total reading, which represents the depth of the beaker:
Total reading = Main scale reading + Vernier scale reading Total reading = 64 mm + 0.4 mm = 64.4 mm
Convert Back to Centimeters Finally, since the question asks for the depth in centimeters, we convert the total reading back from millimeters to centimeters. We know that 1 mm = 0.1 cm, so:
Depth in cm = 64.4 mm * 0.1 cm/mm = 6.44 cm
Final Answer Therefore, the depth of the beaker is 6.44 cm.
Examples
Vernier calipers are commonly used in engineering and manufacturing to precisely measure the dimensions of objects. For example, a machinist might use vernier calipers to measure the diameter of a bolt or the thickness of a metal plate to ensure it meets the required specifications. The vernier scale allows for more accurate measurements than can be obtained with a standard ruler, making it an essential tool for quality control and precision work. The ability to accurately measure dimensions is crucial in ensuring that parts fit together correctly and that products function as intended. This ensures precision and accuracy in various applications, from building construction to scientific experiments.
