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 6.40 mm 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.

The precise depth of the beaker, calculated using the main scale and vernier scale readings, is 0.0108 meters or 10.8 millimeters. This was determined by adding the main scale reading to the vernier scale reading. The conversion of all measurements into compatible units was essential for accurate results.
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Answered by Anonymous | 2025-07-04

Convert the vernier constant to meters: 1.1 mm = 0.0011 m .
Calculate the vernier scale reading: 0.0011 m × 4 = 0.0044 m .
Add the main scale reading and the vernier scale reading: 6.40 m + 0.0044 m = 6.4044 m .
The precise depth of the beaker is 6.4044 m ​ .

Explanation

Problem Analysis We are given the main scale reading, the vernier constant, and the vernier scale division that aligns with a main scale division. We need to find the precise depth of the beaker.

Convert Units First, convert the vernier constant from millimeters to meters: 1.1 mm = 1.1 × 1 0 − 3 m = 0.0011 m

Calculate Vernier Scale Reading Next, calculate the vernier scale reading by multiplying the vernier constant by the division number that aligns with a main scale division: V er ni er sc a l e re a d in g = V er ni er co n s t an t × D i v i s i o n n u mb er V er ni er sc a l e re a d in g = 0.0011 m × 4 = 0.0044 m

Calculate Total Depth Then, add the main scale reading and the vernier scale reading to find the total depth of the beaker: T o t a l d e pt h = 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 d e pt h = 6.40 m + 0.0044 m = 6.4044 m

Final Answer Therefore, the precise depth of the beaker is 6.4044 m.


Examples
Vernier calipers are used in various fields, such as engineering, manufacturing, and scientific research, to make precise measurements of objects. For example, a mechanical engineer might use vernier calipers to measure the dimensions of a machine part to ensure that it meets the required specifications. Similarly, a scientist might use vernier calipers to measure the diameter of a cell or the thickness of a thin film.

Answered by GinnyAnswer | 2025-07-04