Question Video: Measuring the Diameter and Thickness of a Coin Physics

The diameter and thickness of a coin are measured to be 2.4 cm and 2.36 mm respectively. Which of the following tools can be best used to measure these lengths? [A] A standard meter [B] A meter tape [C] A regular ruler [D] A vernier caliper


Video Transcript

The diameter and thickness of a coin are measured to be 2.4 centimeters and 2.36 millimeters, respectively. Which of the following tools can be best used to measure these lengths? (A) A standard meter, (B) a meter tape, (C) a regular ruler, or (D) a vernier caliper.

Before we look at these individual tools though, let’s look at the coin first. A coin’s diameter is how wide it is from one end to the other, which in this case is 2.4 centimeters. But coins are not just flat circles which usually depict people who are very rich and very dead. No, they also have a thickness to them. Looking at it from the side, a coin’s thickness is the distance from the front face to the back face of the coin, which is given as 2.36 millimeters. So the tool that can best measure these lengths has to be able to measure centimeters, millimeters, and fractions of millimeters.

Let’s start by looking at the standard meter. The standard meter is, as the name might imply, one meter long, or exactly 100 centimeters. And every single one of these centimeters are marked, all the way up to 100. And in between the centimeter markings are millimeter markings, which means that the shortest distance the standard meter can accurately measure is one millimeter. This means the standard meter would work great for measuring the diameter of the coin, since it’s 2.4 centimeters. Or since one-tenth of a centimeter is equal to one millimeter, another way we can put 2.4 centimeters is as two centimeters and four millimeters, both of which can be measured on the standard meter.

However, there is still a problem with measuring the thickness of the coin, since the standard meter can only measure full millimeters and not fractions of millimeters. So the standard meter is probably not the best choice. These same principles apply for the regular ruler as well, since it’s just like a meter stick, except shorter. It still only measures centimeters and full millimeters, meaning it’s not the best tool for measuring this coin.

So let’s look at the meter tape then. It has markings for centimeters and in between those markings for full millimeters, just like the regular ruler and standard meter. This means that the only tool that we have left that could be the best tool is the vernier caliper.

Unlike the other three tools, the vernier calipers have two scales, the main scale, located here, which measures centimeters and millimeters, just like our first three tools. But there’s the other scale too, called the vernier scale. The vernier scale is used to measure in between each millimeter marking on the main scale and has an accuracy of up to 0.02 millimeters. This vernier scale accuracy allows us to measure the fractions of millimeters needed to measure the thickness of this coin. And the main scale of this vernier caliper still allows us to measure the diameter of the coin. So we can measure both the thickness and the diameter using just the vernier calipers.

Because of this, the answer for “Which of the following tools can be used to best measure these lengths?” is (D) a vernier caliper.

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