The percentage error for the comparisons would be affected if the value of g used in the calculation is different from the actual value of g at the place where the experiment is performed. The percentage error is calculated as the difference between the experimental and theoretical values, divided by the theoretical value, and multiplied by 100. If the value of g used in the calculation is not accurate, then the experimental values would be different from the actual values, and hence the percentage error would be affected.
To test this, let's consider an example:
Suppose the theoretical value of force is F = mg, where m = 2 kg and g = 9.80 m/s². The experimental value of g is measured to be g' = 9.83 m/s². The force is measured to be F' = 19.6 N.
The percentage error is given by:
% error = [(F' - F)/F] x 100
Substituting the values, we get:
% error = [(19.6 - 19.6)/19.6] x 100 = 0%
Now, if we leave g as a symbol in the calculation of the percentage error, we get:
% error = [(F' - F)/(mg)] x 100
Substituting the values, we get:
% error = [(19.6 - 19.6)/(2 x 9.80 x g)] x 100
Simplifying, we get:
% error = 0.51/g
So, we can see that the percentage error is inversely proportional to the value of g. Hence, if the actual value of g is slightly different from the value used in the calculation, the percentage error would be affected.