7.22 The speed of propagation of a surface wave in a liquid of depth much greater than λ is given by i need clear ans by hand and solve very very fast in 20 min and thank you | DYBALA = = V= gλ 2п + where g acceleration of gravity, A wavelength, p = density. Y surface tension. Compute the group velocity of a pulse in the long wavelength limit (these are called gravity waves). 2πΥ βλ =

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What is “fractional error” for the following formula? Z= 2/3 X2Y3  ,  X= 7m , Y= 4m,   σx=0.2m  ,  σy=0.1m σZ=?

5. a) Find the Green's function for Poisson's equation for the exterior of a sphere of radius a and use it to solve Poisson's equation V₁ = −4лp(r) in the region outside the sphere, i.e. r > a, with the boundary condition (r = a, 0, 0) = F(0, 0), where F(0, 0) is a given function. b) Assume the sphere consists of two metal hemisphered separated by a thin layer of insulator and that the two hemispheres are maintained at potentials +V and -V by a battery inside the sphere. Take p = 0 outside the sphere. Use the formula of part a) to find the potential along the axis above the middle of the hemisphere at potential +V.