Aim:

To study variation of time period of a simple pendulum of a given length by taking bobs of same size but different masses and interpret the result.

Apparatus:

1. A Clamp With Stand
2. Bob with Hook of Different Masses
3. Split Cork
4. Stop Clock/Stop Watch
5. Vernier Callipers
6. Cotton Thread
7. Half Meter Scale

Theory:

See Experiment 6.

The time period (T) of a simple pendulum for oscillations of small amplitude, is given by the relation,

T = 2π√(L/g) or T2 = (4π2/g) × L

∴ T ∞√L and T ∞ 1/(√g)

From the above equation, it clearly indicates that the time period of a simple pendulum is independent of mass i.e. for the same value of L and g, the time period of two bobs of different masses will be the same.

Procedure:

1. Choose any three bobs of known masses and determine their radius as in Experiment 1.
2. Now, arrange the experiment set up for first bob (say mass m1) with any effective length of simple pendulum (say 90 cm) as explained in Experiment 6. The effective length of the simple pendulum will be kept same in each case.
3. Record average time taken for 20 or 25 oscillations by the simple pendulum by performing step 4 to 15 as explained in Experiment 6.
4. Calculate the time periods for each bob and record them in table 7.1.

Observations:

Vernier constant

Vernier constant of the vernier callipers, V.C. = ______________ cm

Zero error, ±e = _____________cm

Least count of stop clock = ____________s

Zero error of stop clock = ___________s

Table 7.1 Determination of time-periods for same lengths of the different pendulum.

Graph:

See Experiment 6.
 

Result:

               For the same value of effective length and acceleration due to gravity, the time period of bobs for different masses are same.

Precautions :

1. The thread should be very light and strong.
2. The point of suspension should be reasonably rigid.
3. The pendulum should oscillate in the vertical plane without any spin motion.
4. The floor of the laboratory should not have vibration, which may cause a deviation from the regular oscillation of the pendulum.
5. The amplitude of vibration should be small (less than 15) .
6. The length of the pendulum should be as large as possible in the given situation.’
7. Determination of time for 20 or more oscillations should be carefully taken and repeated for at least three times.
8. There must not be strong wind blowing during the experiment.

Reference:

1. http://www.ncert.nic.in/
2. https://www.learncbse.in/

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