1. The equipment shown in the diagram was used by a student to investigate the variation with volume, of the pressure p of air, at constant temperature. The air was trapped in a tube of constant cross-sectional area above a column of oil.

The pump forces oil to move up the tube decreasing the volume of the trapped air.

(a) The student measured the height H of the air column and the corresponding air pressure p. After each reduction in the volume the student waited for some time before measuring the pressure. Outline why this was necessary.

(b) The following graph of p versus 1/H was obtained. Error bars were negligibly small.

The equation of the line of best fit is p=a+b/H.

Determine the value of b including an appropriate unit.

(c) Outline how the results of this experiment are consistent with the ideal gas law at constant temperature.

(d) The cross-sectional area of the tube is 1.3×10-3m2 and the temperature of air is 300 K. Estimate the number of moles of air in the tube.

(e) The equation in (b) may be used to predict the pressure of the air at extremely large values of 1/H. Suggest why this will be an unreliable estimate of the pressure.


2. (a) In a simple pendulum experiment, a student measures the period T of the pendulum many times and obtains an average value T = (2.540 ±0.005) s. The length L of the pendulum is measured to be L = (1.60 ±0.01) m.

Calculate, using g=4π2l/t2, the value of the acceleration of free fall, including its uncertainty. State the value of the uncertainty to one significant figure.

(b) In a different experiment a student investigates the dependence of the period T of a simple pendulum on the amplitude of oscillations θ. The graph shows the variation of T/T0 with θ, where T0 is the period for small amplitude oscillations.

The period may be considered to be independent of the amplitude θ as long as T-T0/T0<0.01.Determine the maximum value of θ for which the period is independent of the amplitude.




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