Question

Albert Einstein is pondering how to write his (soon- to-be-famous) equation. He knows that energy E is afunction of mass m and the speed of light c, but he doesn’t know the functional relationship (E = m2c? E =mc4?). Pretend that Albert knows nothing about dimensional analysis, but since you are taking a fluidmechanics class, you help Albert come up with his equation. Use the step-by-step method of repeatingvariables to generate a dimensionless relationship between these parameters, showing all of your work.Compare this to Einstein’s famous equation—does dimensional analysis give you the correct form of theequation?

Answer 1

Answer:

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Explanation:

come everybody

Answer 2

Given info : Energy, E is a function of mass, m and the speed of light , c.

we have to find the relation between E, m and c using dimensional analysis. and comparing it with Einstein famous formula.

solution : E is energy we know, unit of energy is Joule or kgm²/s²

so dimension of E = [ML²T¯²]

dimension of mass , m = [M]

dimension of speed of light, c = [LT¯¹]

let relation between E, m and c is ..

E = m^x c^y , where x and y are real numbers

putting their dimensions we get,

[ML²T¯²] = [M]^x [LT¯¹]^y

⇒[ML²T¯²] = [M^x L^y T^-y]

on comparing we get,

x = 1, y = 2

Therefore relation between E , m and C is E = mc²

so the relation we found is the same formula of Einstein. hence it is clear that dimensional analysis give us the correct form of equation.