# 1.1 Length and time \$

Length and time: Measuring or making measurements is very important in Physics. Without numerical measurements, physicists would have to rely on descriptions, which could lead to inaccurate comparisons.

We use different instruments, such as rules to measure lengths, measuring cylinder to measure volume and clocks or stopwatches to measure time. A physicist will always take care to make the measurements as accurate as possible.

Least count of a measuring instrument

Before learning to measure any physical quantities such as length and time, we need to learn about “least count” of any instrument. The least count of an instrument is the smallest measurement that can be taken accurately with it.

For an instrument provided with one scale, the least count is the value of one division on its scale. For example, the least count of a meter rule is 1 mm ( or 0.01 cm).

Measurement of length with a meter rule

The length is measured with the help of a meter rule/scale. It is graduated to read up to one millimeter. While measuring length with it, the following precautions should be observed.

1) One should measure from the graduation other than ‘0’ marked at one end to avoid due to wear and tear of this end. The correct length is obtained by subtracting the marking observed at one end from that observed at the other end.

2) The eye must be kept vertically above the end of the object and the corresponding graduation in the line of sight should be read. This avoids parallax error due to the thickness of the scale.

Exam Tip – This is all pretty basic stuff. You should be familiar with the ideas on uncertainties and significant figures from using the ideas throughout the course. This is almost an introduction to the course.

To use a measuring cylinder, first make sure that the cylinder is standing on a level table. Then make sure the eye is same level as the liquid inside the cylinder. The surface of most liquids will bend up or down near the walls of measuring cylinder. This bend shape is known as meniscus.  However, most of the surface is flat, and measurements are made to this flat surface. Some measuring cylinders  have unusual scales, and one division may represent an unexpected quantity, perhaps 0.5  or 2. Check this carefully.

A volume of 1mL is same as a volume of 1

1000  = 1000mL = 1L

For measuring large volumes we also use the cubic meter.

1 = 1000L = 1 000 000

The Micrometer

The micrometer is a precision measuring instrument, used by engineers. Each revolution of the rachet moves the spindle face 0.5mm towards the anvil face. The object to be measured is placed between the anvil face and the spindle face. The rachet is turned clockwise until the object is ‘trapped’ between these two surfaces and the rachet makes a ‘clicking’ noise. This means that the rachet cannot be tightened anymore and the measurement can be read.

1. Read the scale on the sleeve. The example clearly shows12 mm divisions.

2. Still reading the scale on the sleeve, a further ½ mm (0.5) measurement can be seen on the bottom half of the scale. The measurement now reads 12.5mm.

3. Finally, the thimble scale shows 16 full divisions (these are hundredths of a mm).

The final measurement is 12.5mm + 0.16mm = 12.66

The least count of micrometer is 0.01mm or 0.001 cm.

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