1. A student investigates the oscillation of a horizontal rod hanging at the end of a vertical string. The diagram shows the view from above.

The student starts the rod oscillating and measures the largest displacement for each cycle of the oscillation on the scale and the time at which it occurs. The student begins to take measurements a few seconds after releasing the rod.

The graph shows the variation of displacement x with time t since the release of the rod. The uncertainty for t is negligible.

(a) On the graph above, draw the line of best fit for the data.

(b) Calculate the percentage uncertainty for the displacement when t = 40 s.

(c) The student hypothesizes that the relationship between x and t is x = a/t where a is a constant.

To test the hypothesis x is plotted against 1/t as shown in the graph.

(i) The data point corresponding to t = 15 s has not been plotted. Plot this point on the graph above.

(ii) Suggest the range of values of t for which the hypothesis may be assumed to be correct.


2. A student measures the refractive index of the glass of a microscope slide.He uses a travelling microscope to determine the position x1 of a mark on a sheet of paper.He then places the slide over the mark and finds the position x2 of the image of the mark when viewed through the slide. Finally, he uses the microscope to determine the position x3 of the top of the slide.

The table shows the average results of a large number of repeated measurements.

(a) The refractive index of the glass from which the slide is made is given by x3-x1/x3-x2


(i) the refractive index of the glass to the correct number of significant figures,ignoring any uncertainty.

(ii) the uncertainty of the value calculated in (a)(i).

(b) After the experiment, the student finds that the travelling microscope is badly adjusted so that the measurement of each position is too large by 0.05 mm.

(i) State the name of this type of error.

(ii) Outline the effect that the error in (b)(i) will have on the calculated value of the refractive index of the glass.

(c) After correcting the adjustment of the travelling microscope, the student repeats the experiment using a glass block 10 times thicker than the original microscope slide.Explain the change, if any, to the calculated result for the refractive index and its uncertainty.




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