Question

For a hypothetical model, total energy of an electron is given as . Total energy = Ar2 + BFt Bv2 where r = distance of electron, F = force on electron, v = speed of electron. Choose CORRECT dimensional formulae of A/C​

Answer 1

Answer:

dimensional formulae of A/C = $[\frac{A}{C}] =[T^{-2}]$

Explanation:

Total energy = $Ar^2 + BFt+ Cv^2$

Principle of homogeneity of dimensions says that, an equation is dimensionally correct if the dimensions of the terms on either side of the equation are the same.

Dimensions of energy = $[ML^2T^{-2}]$

This means all the terms of this equation have the dimensions $[ML^2T^{-2}]$

Equating dimensions of each term with the dimensions of Energy,

$\implies [Ar^2] =[ML^2T^{-2}]\\\implies[A] =\frac{[ML^2T^{-2}]}{L^2}=[MT^{-2}]$

and

$\implies [Cv^2] =[ML^2T^{-2}]\\\implies[C] =\frac{[ML^2T^{-2}]}{L^2 T^{-2}} = [M]$

Dimensions of A/c:

$\implies [\frac{A}{C}] =[MT^{-2}]\\\implies[\frac{A}{C}] =[T^{-2}]$

dimensional formulae of A/C =$[T^{-2}]$

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