Page 75 - Physics - XI

Principle/Theory

According to the principle of moments, "If a body is free to rotate about a fi xed axis, then in equilibrium,
the sum of the clockwise moments is equal to the sum of the anticlockwise moments."
Let m be the mass of the given body. Let a metre scale be supported on a sharp wedge at its centre of gravity
G. If unknown mass m of weight W = mg is suspended at a distance a on one side of the centre of gravity
and a known standard mass M of weight W = Mg is suspended at a distance b on the other side of the centre
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of gravity in such a way so that the metre rod is balanced, i.e. it remains horizontal as shown in Fig. 2.1.
Now, by applying the principle of moment, we have
W × a = W × b or (mg) × a = (Mg) × b
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(Mg ) b× b
or m = or m = M
ga a

Procedure
1. Put the sharp wedge on the wooden block so that suffi cient space remains below the scale for hanging
weights and body of unknown mass. With the help of a spirit level, set the level of the wedge horizontal.
2. Now, place the scale on the wedge with its graduated face up.
3. Now, adjust the position of the scale so that the scale remains balanced, i.e. it remains in horizontal
position, when no weights are suspended. In this position, the centre of gravity of the scale is just
above the wedge. This is called the equilibrium position of the scale. Record the position of the wedge
on the scale.
4. This reading gives the position of centre of gravity G of the metre scale. During the experiment the
metre scale is always placed on this position of the centre of gravity G on the wedge.
5. Now, suspend the unknown weight W = mg on the left side of the wedge and a known standard weight

W = Mg on the right side of the wedge with the help of the cotton thread as shown in Fig. 2.1.
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6. Now, adjust the position of unknown mass m so that the scale gets balanced in the horizontal position.
7. When the horizontal position of the metre scale becomes stable, record the position of body of the
unknown mass A, known mass B, and centre of gravity of the scale G on the metre scale. Note AG = a

and GB = b.
8. Repeat the steps 3, 4, 5, 6, and 7 at least three times with a slightly lighter and a slightly heavier weight.
Record the observations in the observation table.

Observations
Position of the centre of gravity of the scale = G = _____ cm

Table for the determination of unknown mass
S. No. Mass of the body Distance of body of Distance of body of Mass of unknown
suspended to balance known mass from the unknown mass from body
the metre scale, M (g) wedge the wedge, mg =() Mb
(known mass) b (cm) a (cm) a

1.
2.
3.
4.

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