ICSE Class 7 Physics Chapter 1 Measurement

Measurement

Syllabus

1. Mass and Weight - The difference between them - units used - spring-balance, beam-balance.

2. Density - definition - units of measurement - simple calculations based on the formula: D = M / V - variations in the density of gases and liquids with temperature - convection currents (in liquids/gases) arise as a result of this - floating and sinking (with reference to density).

Using a spring-balance / beam-balance (D).

Using a density-bottle to find the density of liquids (D).

Mass And Weight

The mass of a body is the quantity of matter the body contains, regardless of its volume and size. Mass of a body does not change due to any force acting on it.

The earth has a unique property to attract every object towards its centre regardless of its shape, size, state, volume, temperature, etc. This is called gravitation of earth.

The weight of a body is the force with which earth attracts the body towards its centre i.e., it is a measure of the force of gravity of earth acting on the body. It always acts vertically downwards.

Remember, mass and weight are not the same.

Mass remains constant and has the same value at different places. Weight however, varies from place to place. The value of weight depends upon the location of the body in the gravitational field of the earth or other heavenly bodies. Thus, the mass of a body on the surface of the moon is same as that on the surface of the moon. For example, if you go to moon your mass remains same, but your weight measures \(\frac{1}{6}\) of previous weight, since moon's gravity is \(\frac{1}{6}\) that of earth.

Unit Of Mass

According to the Standard International System (S.I.) of units, the unit of mass is kilogram (kg). In CGS system, the unit of mass is gram (g).

One kilogram is the mass of one litre (1000 ml) of pure water at 4°C.

The sub-units of mass are gram (g) and milligram (mg), etc.

\(1 \text{ g} = \frac{1}{1000} \text{ kg} = 10^{-3} \text{ kg}\)

\(1 \text{ mg} = \frac{1}{1000} \text{ g} = 10^{-3} \text{ g} = 10^{-6} \text{ kg}\)

= a millionth part of a kg.

Higher units of mass are quintal and metric tonne, etc.

\(1 \text{ quintal } (q) = 100 \text{ kg}\)

\(1 \text{ metric tonne } (t) = 1000 \text{ kg}\)

Fundamental particles like protons, neutrons and electrons are expressed in atomic mass unit (a.m.u) or unified atomic mass unit (u).

\(1u = 1.66 \times 10^{-27} \text{ kg}\)

However, if you ask for any substance in liquid like, petrol, milk, etc. it is measured by volume in litre.

Measurement Of Mass

We measure the mass of an object by comparing it with a standard mass, generally called weight. These weights are made of iron or brass.

Remember, that these weights have a different meaning than the term 'weight' as used in physics.

We measure mass of a body with the help of a balance. There are several kinds of balances such as a beam balance, a physical balance, a platform balance, a digital balance, and a weighing scale. Normally, we use a beam balance to measure mass.

Beam Balance

The commonly used beam balance is shown in Fig. 1.1. This balance consists of a straight rod of metal. Two pans equal in mass are suspended at the ends of the rod by means of strings or iron chains of equal lengths and mass. Also these pans are suspended at equal distances from the centre of the beam. The beam-balance is suspended through its centre (middle point of the rod) with the help of an iron loop and a pointer is fixed at the centre between the iron loop. If we hold up the balance, and there is nothing on either pan, the rod is horizontal whereas the pointer is vertical.

The commonly used beam balance is shown in Fig. 1.1. This balance consists of a straight rod of metal. Two pans equal in mass are suspended at the ends of the rod by means of strings or iron chains of equal lengths and mass. Also these pans are suspended at equal distances from the centre of the beam. The beam-balance is suspended through its centre (middle point of the rod) with the help of an iron loop and a pointer is fixed at the centre between the iron loop. If we hold up the balance, and there is nothing on either pan, the rod is horizontal whereas the pointer is vertical.

Principle Of A Beam Balance

According to the principle of a beam balance, two bodies of equal or same mass would secure a balance on the beam balance having arms of equal length and pans of equal masses.

Characteristics Of A True Beam Balance

A true beam balance has the following characteristics:

1. Both the arms must be of equal length.

2. Both the pans must be of equal mass.

3. On lifting up the beam balance, without putting anything on either pan, the rod should be horizontal and pointer vertical.

Working Of A Beam Balance

When we use a beam balance, first of all we see that on holding up the balance without putting anything on either pan, the rod is horizontal and pointer should be vertical. Then we keep the body whose mass is to be measured on the right pan and the standard weights are placed on the left pan. The weights on the left pan are adjusted in such a way that the rod again takes the horizontal position on holding up the balance.

Thus, the sum total of the standard weights placed on the left pan gives us the mass of the body.

Some shopkeepers use the grocer's balance (Fig. 1.2) for weighing articles like sugar, rice, pulses, vegetables, etc.

Unit Of Weight

The unit of weight in the Standard International System (S.I.) is Newton (N) while in CGS system or the sub-unit of weight is dyne.

\(1N = 10^5 \text{ dyne}\)

The weight of a body is very often expressed in kgf and gf.

The weight of a body of mass 1 kg is equal to 1 kgf. Likewise, the weight of a body of mass 1 g is equal to 1 gf.

\(1 \text{ kgf} = 9.8 \text{ N} (\approx 10N)\)

\(1 \text{ gf} = 980 \text{ dyne} (\approx 1000 \text{ dyne})\)

Measurement Of Weight

Weight is measured by an instrument called spring balance as shown in Fig. 1.3. It consists of a spring enclosed in a metallic case. The upper end of the spring is fixed at the top of the case while the lower end of the spring is attached to a pointer and a long rod with a hook at its end. The metallic case has with a slit cut along its length through which the pointer projects out and the rod can be seen. The metallic case is graduated at the top with zero mark and the weights in the increasing order in downward direction (e.g., 0 gf, 100 gf, 200 gf, 300 gf, 400 gf, 500 gf, ...... 1 kgf, etc.). Till no object is suspended on the hook, the pointer reads zero. When an object is suspended on the hook, the spring extends and the pointer moves down the scale. A ring is provided at the top of the metallic case to hang it from a rigid support.

Principle Of A Spring-balance

When a load is suspended on the hook at the lower end of the spring, the spring elongates due to the weight of the load suspended. If the weight suspended is increased, the spring will elongate further. Thus, spring-balance works on the principle that more the weight is attached (or more the force is applied) to the spring, the more it gets stretched (elongated).

Activity 1

Take three empty cans A, B and C of equal size and equal weight. Suspend them separately with a support using springs. Now lift the cans upwards by one. You will see that lifting the empty cans is easy and the extension of the springs in all the three cans is equal.

Now fill can A half with water and lift the cans (A) and (B). You will notice that the extension of the spring in can A is more than in can B. Now fill can C almost completely with water and lift the cans (A), (B) and (C) upwards.

What do you observe?

You will see that the spring attached with can (C) is stretched more than both cans (A) and (B). But the spring attached with can (A) will stretch more than the spring attached to can (B). Also, greater effort is needed to lift the can completely filled with water, i.e., can C. We conclude that, more the weight, more will be the extension in the spring.

Working Of A Spring-balance

To use a spring-balance, first hang it vertically from a rigid support. Make sure that the pointer reads zero. Then the object whose weight is to be measured is suspended on the hook, attached to the spring balance. The pointer moves down. Wait till the pointer becomes stationary. Then read the position of the pointer through the calibrated scale. This reading gives the weight of the object. Fig. 1.4(c) shows that weight of the object hanging from a spring balance is 300 gf.

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