Assignment:
Q1. Two pendula of equal length l but different masses m and 2m swing in vacuum inthe gravitational field with the acceleration g. Use dimensional analysis to determinewhich pendulum will have a longerperiod.
Q2. The analogue of the elastic modulus for fluids (the bulk modulus) is given by E = Ρc2, where Ρ is the fluid density and cis the the sound speed. Then the relationship between the stress and strain in the fluid can be presented by the formula p = Ρc2ε (cf. with the analogous formula for the elastic materials given is E/c2=kΡ).Influids,however, there are also the effects of viscosity, which gives an additional stress, which is proportionalnot to strain, but to the rate of strain change in time ~dε/dt. Thus, a more general equation relatesa pressure and astrain:
p = Ρc2ε + μdε/dt ,
where μ is the molecular viscosity of a fluid.
Assuming that p is constant, find the relaxation time for the strain as described by this equation and the equilibrium state for the strain.
Hint. The relaxation time is defined as the time when the quantity of interest decays with time in the typical degree. For example,if the quantity is described by exponential function exp(–t/T), then the relaxation time T is the time when the quantity decay’s in etimes.
Provide complete and step by step solution for the question and show calculations and use formulas.