4 00.5 points 1Previous Arswers Tipier 1.P.00a My Notes Ask Your Force has dimen

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4 00.5 points 1Previous Arswers Tipier 1.P.00a My Notes Ask Your Force has dimensions of mass times acceleration. Acceleration has dimensions of speed divided by time. Pressure is defined as force divided by area. What are the dimensions of pressure? Express in terms of the SI base units kilogram, meter, and second. (use the following as necessary: kg, m, and s.) Use the definitions of force and pressure, together with the dimensions of mass, acceleration, and length, to find the dimensions of pressure. Then express pressure in terms of the SI base units by substituting the base units for mass, acceleration, and length in the definition of pressure My Notes Asx Your Teacher 9. 010.5 points l Frevious Answers Toes 1.P044. Kepler's third law relates the period of a planet to its radiusr, the constant G in Newton's law of rviation (Gmm22) and the mass of the sun Ms. What combination of these factors gives the correct dimensions for the period of a planet? Use any variable or symbol stated above along with the following as necessary: C a dimensionless constant.) Express the period of a planet as the product of the factors r,G, and Ms (each raised to a possibly negative and fractional power) and then perform dimensional analysis to determine the values of the exponents.

Explanation / Answer

a)

Pressure = Force / area

dimensions of force = m L t^-2

dimensions of area = L^-2

So, pressure = [m L t^-2] / [L^-2]

= m L^3 t^-2 <------- answer

b)

Using Kepler's 3rd Law,

T^2/r^3 = (4*pi^2) / (G *Msun)

So, T^2 =  ((4*pi^2) / (G *Msun))* r^3

So, T = sqrt( ((4*pi^2) / (G *Msun))* r^3)

So, dimensions of T = G^-1/2 . r^3/2 . Ms^-1/2 <------ answer

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