Which of the following expression can be deduced on the basis of dimensional analysis? (All symbols have their usual meanings)

Step-by-step solution

Option (1): (x=A ( t) ) - (A ) : displacement ( [L] ) - ( ( t) ) : dimensionless E) Dimensionally correct. However, dimensional analysis cannot deduce the presence of a trigonometric function like cosine. Cannot be deduced via dimensional analysis. Option (2): (N=N₀ e^ - t ) - ( N₀ ) : number of nuclei ( ) dimensionless - ( ) : decay constant ( [T⁻¹ ] ) - ( t ) : dimensionless ( ) exponential argument is fine E. Again, though dimensionally correct, the exponential form can't be derived using dimensional analysis. C