Live practice

At what temperature does argon have the same rms atomic speed as helium at −20°C? Use M_Ar=39.9 u and M_He=4.0 u.

Level mercury surfaces balance \(10.0\,\mathrm{cm}\) of water against \(12.5\,\mathrm{cm}\) of methylated spirit. Find the spirit's specific gravity.

A steel cable of radius \(1.5\,\mathrm{cm}\) must not exceed a stress of 10⁸ Pa. Find its maximum supported load.

A body starts from rest and moves in one dimension with constant acceleration. To which power of time is the instantaneous power proportional?

A 20,\(000\,\mathrm{kg}\) rocket rises initially with acceleration \(5.0\,\mathrm{m\,s}\)⁻². Calculate its initial thrust, taking \(g=10\,\mathrm{m\,s}\)⁻².

A cyclist goes from the centre of a circular park of radius \(1\,\mathrm{km}\) to the edge at P, follows the quarter-circle arc from P to Q, and returns from Q to the centre in

A \(1800\,\mathrm{kg}\) car has axles \(1.8\,\mathrm{m}\) apart and its centre of gravity is \(1.05\,\mathrm{m}\) behind the front axle. Find

Two fair dice are thrown. Find the probability that their sum is 8.

A fair coin is tossed twice. Find the probability that at least one tail occurs.

A series has mean 50 and standard deviation 8. Find its coefficient of variation.