Question

1 (a) (i) a force - extension graph for a spring which obeys hooke’s law was drawn and it was observed that : 1. the plotted points did not follow a straight line 2. the intercept was not zero state the error associated with each observation. (ii) explain whether or not a systematic error can be eliminated by averaging repeated readings.

Explanation:

Step1: Analyze non - straight line

For a spring obeying Hooke's law, the force - extension relationship is $F = kx$ (where $F$ is force, $k$ is spring constant and $x$ is extension), which is a linear relationship. If the points do not follow a straight line, it is likely due to random errors in measurement. Random errors cause scatter in the data points.

Step2: Analyze non - zero intercept

A non - zero intercept indicates a systematic error. For example, if there is an initial force already acting on the spring before measurements start (like a pre - tension), or an incorrect zero - setting of the measuring instrument for extension, it will cause the intercept to be non - zero.

Step3: Answer part (ii)

Systematic errors are consistent in nature. Averaging repeated readings only reduces the effect of random errors. Since systematic errors are either due to instrument inaccuracies or experimental setup issues that are consistent throughout the measurements, averaging repeated readings will not eliminate systematic errors.

Answer:

(i) Non - straight line: Random error; Non - zero intercept: Systematic error.
(ii) No, a systematic error cannot be eliminated by averaging repeated readings because systematic errors are consistent and not random in nature.