Question

convert 10joule of energy using dimensional analysis

Answer 1

It's conversion factor between joule and erg
Joule and erg are the unit of work or energy.
Joule is S.I unit where as erg is C.G.S unit.
We will find dimension of work first.
Work = f×s =m×a×s =Kgm^2/s^2
= M^1 L^2 T^-2

Now let x be the conversion factor 1J =x erg
1(M^1 L^2 T^-2) = x(M^1 L^2 T^-2)
1 Kg × m^2 / s^2 = x gm×cm^2/s^2
Therefore
10^3 gm × 10^4 cm ^2
= x gm × cm^2
= 10^3 × 10^4 = x
Therefore x = 10^7
Therefore 1 joule is 10^7 erg

Hope you will find this helpful. ...