i have problems with applied physics calculations,i've been working on these questions 4 3 days now.any help?

Question

1.assuming that the period of vibration of a tunning fork depends upon the lenght of the prong and on the density and young's modulus of the material,find by method of dimensions,a formula for the period of vibration[define young's modulus y=stress/strain=(force/area)(extension/original lenght).

2.assuming that the critical velocity vc of a viscous liquid flowing through a capillary tube depends upon the radius 'a' of the tube,the density p and the coefficient of viscosity n of the liquid,obtain a relation between vc,p,a and n.[define coefficient of viscosity n as: force/area times (velocity/displacement).

Answer 1

I suggest asking questions to help clarify in your mind the basic concepts involved, rather than beg someone to do your homework. This will prove you've given it some thought.

Answer 2

Just lay out all the dimensions and see what combinations would work.

1.
T, period = time
L, length = length
p, density = mass/volume = mass/length^3
E, modulus = force/area = (mass*length/time^2)/length^2 = mass/(length*time^2)

p/E = mass*length*time^2/(length^3*mass) = time^2/length^2
pL^2/E = time^2*length^2/length^2 = time^2
sqrt(pL^2/E) = sqrt(time^2) = time, and can also be expressed as L*sqrt(p/E)

So the period varies with length and with the square root of the ratio of density to Young's modulus.

I'll start you on the second problem, but I won't complete it.

2.
vc = length/time
a = length
p = mass/length^3
n = (force/area)(velocity/displacement) = ((mass*length/time^2)/length^2)((length/time)/length) = (mass/(length*time^2))(1/time) = mass/(length*time^3)

You need to find a rational expression of a, p, and n that gives you a power of length/time with no mass involved, and then take an appropriate root if necessary.