Page 33 - Physics - XI

A physical balance consists of a light, rigid metal beam balanced at its centre of gravity on a knife edge
made of agate (very hard substance) rest on a fl at agate surface fi xed on the top of a vertical pillar V. Two
similar pans of equal mass are suspended from two knife edges at the end of the beam. A pointer P is
fi xed at the middle of the beam which moves freely in front of a horizontal scale fi xed at the base of the
pillar. S and S are adjusted till the pointer P stands at the centre of the scale, i.e. at zero. A plumbline is
1
2
suspended from the support of the beam. When the pillar is vertical, the plumbline points towards tip T.
Three levelling screws are fi tted at the base to level the balance and made co-planar.

Principle/Theory

The physical balance works on the principle of moment, i.e. when a body is in equilibrium under the action
of a number of forces acting on it in the same plane, the sum of clockwise moments is equal to the sum of
anticlockwise moments.

Let an object of mass m to be weighed is placed in the left pan and standard weight of mass m is put in
R
L
the right pan to keep the beam horizontal. In this condition,
Weight (m g) in the left pan = weight (m g) in the right pan
L R
Since the value of 'g' is constant at the given place.

∴ m = m
L R
Mass of the object in the left pan = Mass of the standard weight in the right pan.

Procedure
1. First of all, adjust the levelling screws at the base so that plumbline hangs exactly over the fi xed

pointed tip T.
2. Lift the beam slowly without any jerk using the lever.

3. Check the position of the pointer on the scale. If it is at zero, the balance is set correctly. If the pointer
shifts more in one direction, turn the adjusting screws S of that side outward (or screw S of other side
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inward) to get the pointer at zero. While turning the screws, do not forget to lower the beam to bring it
in its position of rest.
4. Make a rough guess of the mass of the body. Let the rough mass of the body be about 40 g.

5. Now, put the body in the left pan and add standard masses of 50 g in the right pan. If this mass will
come out to be more than the actual mass of the body, replace 50 g masses in the right pan by 30 g
masses. If the pointer will turn on the other side, it shows that the mass of the body is more than 30 g,
but less than 50 g. Hence, the range in which the mass of the body lies is 30 – 50 g in this case.
30+50
6. Now, try with another standard mass that lies between 30 g and 50 g =40g . There are two

possibilities: 2

(a) mass of the body M, M > 40 g or (b) M < 40 g.
7. Let the pointer indicate that M > 40 g, hence M lies between 40 g and 50 g. Hence, now the range has

been reduced to 10 g.
40 50+
8. Now, again try = 45 g on the right pan and also fi nd whether M > 45 g or M < 45 g. It shows
2
that M < 45 g, then actual mass of the body lies between 40 g and 45 g. Now, the range is reduced to 5 g.

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