Procedure:
- A metal bob is tied to an inelastic string.
- The string is then held while the bob is rotated in a horizontal circular motion.
- The time taken for 20 revolutions is recorded using a stopwatch.
- The radius of the arc is then changed, and readings for the time are taken again.
- The procedure is repeated for 10 different radii (lengths of string) and 5 readings for the time are taken for each radius.
- The data is then used to find the average radius and average time, to find the acceleration due to gravity.
Error Propagation:
-
Error Of Meter Scale = Least count of meter scale ÷ 2 (Analog Instrument)
=
= 0. 05 cm
-
Error of Calculated Time = Least Count ÷ 2 = 0.1 ÷ 2
0.05 s
- Small mass (m) = 18.46 ± 0.01 gms
- Big Mass (M) = 300.00 ± 0.01 gms
Data Collection & Processing:
The data collected by the procedure is recorded and tabulated below:
Now, we can take all the time periods to find the Average Time Period, since
Time average = Time periods of all trials ÷ No. of Trials
For example,
T 2 (average) = (11.60 +12.00 + 11.80 +11.20 +11.0) ÷ 5 = 11.52 ± 0.05 s
Next, the average time period for one oscillation as per every length is calculated by dividing the average time period of that length by a factor of 20.
This is shown in the next table.
Now that we have the time period for one oscillation for every length, we can use this to find the acceleration due to gravity.
Evaluation
The graph above will help us to establish the acceleration due to gravity. We can find the total average time found for all trials.
We have 2 formulas to find the Tension in a string, they are,
T=Mg , and
T= mv2/r
Thus, Mg = mv2/r
Thus, v =
We also have a formula that gives us ‘v’, i.e.
v =
Thus, =
= =
And from this equation we get the formula for acceleration due to gravity, ‘g’
g =
We can thus use this equation to find the value of ‘g’ by substituting the values of the variables ‘m’ ‘M’ ‘r’ and ‘t’
For example, for the first length L1 = 49.00 ± 0.05 cm
g =
=
=
-
Time average = Sum total of average time / Number of trials
= 138.58/ 10
= 13.858
= 13.86 seconds
-
Time range = (Time maximum – Time minimum ) ÷ 2
= (18.10 – 10.90) ÷ 2
= 3.60 seconds
Error / Uncertainty:
Time average + Time range = 13.86 ± 2.05 seconds
Using the calculations from before,
Time average = 13.86
No. of revolutions: 20 revolutions
Thus, Time period for 1 revolution= Time (average) / Number of revolutions
= 13.86 / 20
= 0.693 seconds
Average Radius = (49+50+51+52+53+54+55+56+57+58) / 10
= 53.5 cm
Thus, using the acquired values, we get the acceleration due to gravity as
g = 4×π×r×m ÷ t×M.
= 4π (53.5)2 (18.458) / (14.7)2 (300)
g= 10.25 ms-2
Conclusion:
Thus through the above experiment we find that the acceleration due to gravity is approximately 10.25 ms-2
Evaluation :
As mentioned before, the ideal acceleration due to gravity on the surface of the Earth is considered to be approximately 9.81 ms-2. However, considering the method used above and the surroundings in which it was conducted, the experiment can be called successful.
There are many reasons that would explain the deviation in the value, some of which would be:
- Wind causing improper execution of the experiment
- Ceiling fans deviating the natural path of the arc
- Possible error in the apparatus used, like the weighing scale not being completely accurate
If these factors are to be eliminated, the deviation would certainly reduce, making the value more accurate.
The percentage deviation in the experiment = (Deviation/ 9.81) × 100
= (10.25 – 9.81/ 9.81)×100
= 4.48 %
