A simple pendulum has a light, inextensible string of length L and a bob of mass m. It is set into small–angle oscillations in a laboratory where the acceleration due to gravity is g.
(i) Write the mathematical expression for the time period T of the pendulum under these conditions.
(ii) The bob is replaced by another of mass 2m while every other parameter is kept unchanged. Predict, with suitable reasoning, whether the time period will change and, if so, by what factor.
(iii) Justify physically why the mass of the bob does not influence the time period in the ideal model of a simple pendulum.
(iv) State any one explicit assumption made in deriving the expression quoted in part (i) and explain how violating this assumption could lead to a change in the result obtained in part (ii).