Page 50 - Physics - XI

Clamp
Split S S S
cork P 7 130 cm
Stand Thread P 120 cm
Table P 6 5 110 cm

P 4 100 cm
P 90 cm
3
l′ P 2 80 cm
L P 1 70 cm
Hook
T
O h
r C.G. of G
C 5 cm 5 cm B L=l'+h+r G the bob

Fig. 7.4: Simple pendulum Fig. 7.5: Eff ective length
Principle/Theory

The time period T of a simple pendulum of length L is given by the relation:
L
T = 2π …(1)
g
Here g is the acceleration due to gravity. On squaring equation (1), we have
L
T = 4π 2 g …(2)
2
If we plot a graph between L and T , it will be a straight line.
2
Procedure

1. First of all, fi nd out the Vernier constant (or least count) and zero error of the Vernier Calliper and
determine the mean diameter and hence mean radius of the spherical bob.
2. Tie the hook of the bob to the cotton thread about 150 cm long and the other end of the thread is passed
through the two half pieces of a split cork as shown in Fig. 7.5.

3. Put ink marks P , P , P ______ on the thread at distances of 70 cm, 80 cm, 90 cm, 100 cm, 120 cm from
3
1
2
the centre of gravity of the bob including the height of the hook as shown in Fig. 7.5. These distances
give the eff ective length (L) of the simple pendulum.
(L = l' + h + r).

4. Take a clamp stand and place it on the table in such a way so that the bob is about 2 cm above the
ground. Mark two lines with a piece of chalk just below the bob, one parallel to the edge of the table
and other perpendicular to it. Mark two points B and C on either side of the point of interaction O and
at a distance of about 5 cm as shown in Fig. 7.4.
5. Now, put 130 cm mark at the lower surface of the cork by pulling the thread through the cork pieces.
Adjust the clamp so that the bob is about 2 cm above the ground.

6. Find out the least count of the stopwatch and bring its hands at zero position.
7. Now, displace the bob to one side of its rest point O and release the bob gently so that the bob starts
vibrating in a vertical plane about point O. Make sure that the bob does not spin about its own axis while
vibrating.

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