Paper 3 (Section A + Option A: Astrophysics)

A student determines g using a simple pendulum. Explain why she times 10 oscillations and uses a fiducial marker at the centre of the swing.

Figure 1 shows T² against L. Use it to determine g.

For L = 1.000 m (±0.001 m) the time for 10 oscillations was 20.1 s (±0.2 s). Calculate the percentage uncertainty in g from this single reading.

The student measured L to the top of the bob instead of its centre. Explain the effect on the graph and on her value of g.

Describe how to measure the resistance of different lengths of a wire to determine its resistivity, giving two precautions.

The gradient of a graph of R against L is 12.5 Ω m⁻¹. The diameter of the wire is 0.32 mm ± 0.01 mm. Calculate the resistivity and the percentage uncertainty in the cross-sectional area.

The graph does not pass through the origin. Suggest why, and explain the effect on the value of resistivity.

Describe how to investigate how the first harmonic frequency of a stretched string depends on its tension.

Results:

T / N	2.0	4.0	6.0	8.0
f / Hz	50	71	87	100

Show that the data are consistent with f ∝ √T, using a logarithmic method.

The string length is 1.00 m. Calculate the mass per unit length.

Describe how to investigate the discharge of a capacitor through a resistor.

A graph of ln(V / V) against t is a straight line of gradient −0.0435 s⁻¹. The resistor is 100 kΩ. Calculate the capacitance.

Explain why a graph of ln V against t is more useful than V against t.

Describe how to investigate how the intensity of gamma radiation varies with distance from a source. Include safety precautions and how you would analyse the data.

A refracting telescope has objective focal length 1.20 m and eyepiece focal length 0.040 m. Calculate the angular magnification and the lens separation in normal adjustment.

Explain why large research telescopes are reflectors rather than refractors.

Calculate the minimum angular resolution of a 2.4 m telescope at 550 nm, and give one advantage of a CCD over the human eye.

A star has apparent magnitude 4.2 and is 50 pc away. Calculate its absolute magnitude.

A star has peak wavelength 290 nm. Calculate its surface temperature and state its spectral class. A second star has the same luminosity and a surface temperature of 5000 K. Calculate the ratio of their radii.

Describe the evolution of a star like the Sun from the main sequence to its final state, and show its path on a Hertzsprung–Russell diagram.

The Hα line (656.3 nm) from a galaxy is observed at 669.4 nm. Calculate the galaxy's recession speed.

Taking H₀ = 70 km s⁻¹ Mpc⁻¹, calculate the distance to this galaxy and estimate the age of the Universe.

Give three pieces of evidence for the Big Bang model.

Explain two methods of detecting exoplanets.