You are measuring the diameter of a small steel ball using a vernier caliper. The main scale reading just before the 0 of the vernier caliper is 1.2 cm. The [tex]6^{th}[/tex] line on the vernier scale aligns perfectly with a line on the main scale. Calculate the diameter of the steel ball.
Answer (2)
Identify the main scale reading (MSR) as 1.2 cm.
Calculate the vernier scale reading (VSR) by multiplying the coinciding division (6) by the least count (0.01 cm), resulting in VSR = 0.06 cm.
Add the main scale reading and the vernier scale reading to find the total reading: 1.2 cm + 0.06 cm = 1.26 cm.
Conclude that the diameter of the steel ball is \boxed{1.26 \text{ cm}}.
Explanation
Problem Analysis We are given the main scale reading (MSR) as 1.2 cm. The 6 t h line on the vernier scale coincides with a line on the main scale. We need to calculate the diameter of the steel ball.
Calculate Vernier Scale Reading The least count (LC) of a standard vernier calliper is 0.01 cm. The vernier scale reading (VSR) is calculated by multiplying the coinciding vernier scale division by the least count. Therefore, VSR = 6 * LC = 6 * 0.01 cm = 0.06 cm.
Calculate Total Reading The total reading is the sum of the main scale reading and the vernier scale reading. Total Reading = MSR + VSR = 1.2 cm + 0.06 cm = 1.26 cm.
Final Answer The diameter of the steel ball is equal to the total reading obtained from the vernier calliper. Therefore, the diameter of the steel ball is 1.26 cm.
Examples
Vernier callipers are used in various fields like engineering, manufacturing, and scientific research to precisely measure the dimensions of objects. For example, an engineer might use a vernier calliper to measure the diameter of a pipe to ensure it fits correctly with other components in a plumbing system. Similarly, a machinist might use it to measure the thickness of a metal sheet to ensure it meets the required specifications. In scientific research, vernier callipers can be used to measure the size of biological samples or experimental setups with high precision. The vernier calliper provides a more accurate measurement compared to using a standard ruler.
The diameter of the steel ball is calculated by adding the main scale reading of 1.2 cm to the vernier scale reading of 0.06 cm, resulting in a total of 1.26 cm. Thus, the diameter is 1.26 cm. This measurement is done using a vernier caliper for precision.
;
