I\'m having trouble solving several Dimensional Analysis problems. It would be g

Question

I'm having trouble solving several Dimensional Analysis problems. It would be great if anyone could help explain it step by step. Thanks. Q1. The dimensions of these 4 pysical quantites are: [period of oscillation]=T [m]=M [V]= L^3 [G]=L^(3)*T^2*M^-1 Calculate the exponents, a,b and c assuming T is proportional to m^(a)*V^(b)*G^(c). Inserting the proportionality constant k, write an equation for the period of oscillation ( write =k*m^(a)*V^(b)*G^(c) where you insert the correct value for a,b and c0. The determination of the dimensionless proportionality constant k requires a more refined theory of stellar oscillation, or observation inforation but the interesting dependence upon the physical parameters can be obtained from dimensional considerations alone. Q2. Dimensional analysis of the radius of a black hole. Including the dimensionless the proportionality constant k, write an equation for the radius r of a black hole in terms of the black hole's mass m, the gravitational constant G, and the speed of light c.

Explanation / Answer

a=-1/2 b=-1 and c=1

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