Class 11 Physics practical reading Using a simple pendulum, plot L-T and L-T² graphs. Hence find effective length of second's pendulum using appropriate graphs.

Aim

Using a simple pendulum, plot L-T and L-T² graphs. Hence find effective length of the second's pendulum using appropriate graphs.

Apparatus Required

Metallic bob, vernier callipers, stopwatch thread, a clamp with stand, meter rod.

Theory

A simple pendulum consist of a bob (heavy mass) suspended from a rigid support using an extensible and massless string The time period of a simple pendulum is given by

         T² = (4π²L) /g

L = effective length of the pendulum. g = acceleration due to gravity. 

The effective length of simple pendulum is the distance between the point of suspension and the centre of of the bob. 

It is given by

            L = l+h + r, 

l = length of the string 

h = length of the hook and

r = radius of the bob.

A simple pendulum whose time period is two seconds is called second's pendulum.

Procedure

1. Take a vernier calliper. Find its least count and record it. Also take a stop watch, record its least count and zero error, if any. 

2. Find the mean diameter of the bob using a vernier calliper. Calculate its radius r = d/2 .Find the length h of the hook attached to the bob and record it. 

3. Take cotton thread of about 2 meter length and tie one end with the hook. Put ink marks on it at 70 cm, 80 cm, 90 cm, 100 cm . 

4. Pass the thread through split cork with thread coming out of 70 mark. Tight cork pieces between clamp. 

5. Fix the clamp on a stand kept on table so that bob is just a few centimetres above the floor. Mark a point just below the position of a bob, when it is at rest. 

6. Release the bob above point B on the right of A and start the stop watch. Count 20 vibrations and record the time taken. 

7. Repeat step 6 two more times for the same length. 

8. Loose the cork pieces and pull the thread out to increase its length by 10 cm. Now effective length of pendulum become 80 cm. 

9. Repeat step 6 and 7 to get another set of observations. 

10. Repeat step 8 and then step 6 and 7 to take more sets of observations for lengths 90 cm, 100 cm, 110 cm ........ and record all observations.

Observations

Precautions

1. Use a good stop watch of small least count. 

2. Thread should be in extensible and of neglibible mass. 

3. Point of suspension should be attached to a rigid support. 

4. The bob should not spin during vibration. 

5. Amplitude of the oscillations should be small.

Sources of Error

1. Point of suspension may not be rigid. 

2. The amplitude of oscillation is very large. 

3. The bob spins during oscillation. 

4. There may be delay in starting and stopping of stop watch. 

5. The air currents may disturb vibration.