PHYSICS · Subjective · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
A simple pendulum of length ℓ has a bob of mass m. Its time period is observed to be T0 at a certain location where the acceleration due to gravity is g. The following sequence of changes is then carried out one after another.
Step 1 The length of the pendulum is reduced to 43ℓ.
Step 2 A second identical bob is firmly attached to the first so that the total mass becomes 2m.
Step 3 The pendulum is taken to a hill station where the value of g is 0.96g.
(i) Write the expression for the initial time period T0 in terms of the given symbols.
(ii) Calculate, in symbols, the factor by which the time period changes after each individual step (do not substitute numerical values yet).
(iii) Hence obtain the overall factor by which the time period has changed after all three steps.
(iv) If T0=2.0s, find the final numerical value of the time period after Step 3.