Experimental Physics, Error Analysis and Estimation — Practice

Question 1

Using dimensions, find how the period of a pendulum depends on length L and gravity g.

Accepted Answer

T is proportional to root(L/g); mass cannot appear because only mass carries the mass dimension.

Question 2

What should be plotted to find g from a pendulum experiment, and what is the gradient?

Accepted Answer

T squared against L, with gradient 4 pi squared over g.

Question 3

Estimate the mass of the Earth's atmosphere.

Accepted Answer

Surface pressure 1e5 Pa supports the air column, so M = 4 pi R^2 P/g = 4 pi (6.4e6)^2 (1e5)/9.8, about 5e18 kg.

Question 4

L = 1.00 +- 0.01 m and T = 2.01 +- 0.02 s. Find g = 4 pi^2 L/T^2 with its uncertainty.

Accepted Answer

g = 9.77 m/s2. The relative error is root(0.010^2 + (2 x 0.00995)^2) = 0.022, so g = 9.77 +- 0.22 m/s2.

Question 5

A screw gauge has pitch 0.5 mm and 50 circular divisions. Find the least count.

Accepted Answer

0.5/50 = 0.01 mm.

Question 6

A power law y = k x^n is suspected. How can n be found from data?

Accepted Answer

Plot log y against log x. The graph is a straight line of gradient n and intercept log k.

Question 7

How can the timing error in the pendulum experiment be reduced and why does it matter most?

Accepted Answer

Time 20 or more oscillations and divide, so the fractional error in the period falls. T is squared in the formula for g, so its relative error counts twice and dominates.

Question 8

Name two kinds of error and one way to reduce each.

Accepted Answer

Random error is reduced by repeating and averaging. Systematic error is reduced by calibration or a better method.

Practice — Experimental Physics, Error Analysis and Estimation

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