28th-ipho_questions97

# 28th-ipho_questions97 - 28th International Physics Olympiad...

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Theory Question No.1 Scaling (a) A small mass hangs on the end of a massless ideal spring and oscillates up and down at its natural frequency f . If the spring is cut in half and the mass reattached at the end, what is the new frequency ? (1.5 mark s) f (b) The radius of a hydrogen atom in its ground state is a 0 = 0.0529 nm (the “Bohr radius”). What is the radius of a “muonic-hydrogen” atom in which the electron is replaced by an identically charged muon, with mass 207 times that of the electron? a Assume the proton mass is much larger than that of the muon and electron. (2 marks ) (c) The mean temperature of the earth is T = 287 K. What would the new mean temperature T be if the mean distance between the earth and the sun was reduced by 1%? (2 marks ) (d) On a given day, the air is dry and has a density ρ = 1.2500 kg/m 3 . The next day the humidity has increased and the air is 2% by mass water vapour. The pressure and temperature are the same as the day before. What is the air density ρ now? (2 marks ) Mean molecular weight of dry air: 28.8 (g/mol) Molecular weight of water: 18 (g/mol) Assume ideal-gas behaviour.
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