In an attempt to make the pendulum more durable, a student replaces the usual cotton thread with a thin steel wire of the same length L. The mass per unit length of the wire is λ and the mass of the spherical bob is M.
(i) Identify the ideal assumption regarding the string that is violated by using the steel wire.
(ii) Explain qualitatively whether the presence of the massive wire will increase, decrease, or leave unchanged the time period compared with an ideal simple pendulum of the same length.
(iii) Taking the centre of mass of the wire to be midway along its length, treat the system as two point masses (the bob and an effective mass 2λL located at the midpoint). Show, with suitable reasoning, how this modelling leads to a modification in the dependence of the time period on the total mass of the system.
(iv) If λL=0.10M, estimate the percentage change in the time period relative to the ideal case and comment on whether this change would be easily noticeable in a school laboratory experiment.