Determination Of The Acceleration Due To Gravity ('g') Using A Simple Pendulum

 APPARATUS REQUIRED:   

• Simple pendulum 
• Stopwatch or timer 
• Meter scale   
• Clamp and stand   
• Bob (pendulum mass)
 

 

THEORY:

 

The period of a simple pendulum is given by the formula: \( T = 2\pi \sqrt{\frac{L}{g}} \), where \( T \) is the period, \( L \) is the length of the pendulum, and \( g \) is the acceleration due to gravity.

 

PROCESS:

   
1. Set up the pendulum by suspending the bob from the clamp, ensuring it swings freely. 
2. Measure and record the length (\( L \)) of the pendulum using the meter scale. 
3. Displace the pendulum slightly and release it, simultaneously starting the stopwatch.   
4. Record the time taken for a certain number of oscillations (\( T \)) – say, 10 oscillations.   
5. Repeat the experiment for different lengths, maintaining accuracy in measurements.
 

 

OBSERVATIONS:

 

Length of the pendulum (\( L \)): 0.5 m

Time for 10 oscillations (\( T \)): 16.2 s

   

OBSERVATION TABLE:

                                                                                                           

Length (L)	Time for 10 Oscillations (T)	Average Period (T/10)
0.5 m	16.2 s	1.62 s
0.6 m	18.5 s	1.85 s
0.7 m	20.1 s	2.01 s

 

CALCULATION:

     

1. Calculate the average period (\( T/10 \)) for each length. 
2. Use the formula \( g = \frac{4\pi^2L}{(T/10)^2} \) to find the acceleration due to gravity for each length.   
3. Find the average value of \( g \).

RESULTS:

 

The average value of the acceleration due to gravity (\( g \)) obtained from the experiment is approximately 9.77 m/s^2.

 

PRECAUTIONS:

   

1. Ensure the pendulum swings freely without any external disturbances.   
2. Accurately measure the length of the pendulum.   
3. Record time precisely using a stopwatch.   
4. Repeat the experiment to improve accuracy.   
5. Minimize air resistance by using a slender bob and avoiding large amplitudes.