Answer to Question #126739 in Classical Mechanics for Ashley

Question

Which of the following equations is dimensionally homogenous?

A. F=m(vf - vi)
B. F=1/2 m(vf2-vi2)
C. F=ρVg
D. F=m s / t

Answer 1

We know that the dimensional formula of the force is$=[MLT^{-2}]$

dimensional formula for mass $(m)=[M]$

Velocity $(v)=[LT^{-1}]$

Dimensional formula for the gravitational acceleration $=[LT^{-2}]$

Dimensional formula for the density $\rho =[ML^{-3}]$

Dimensional formula for time $=[T]$

i) From the given question,

$F=m(vf - vi)$

Now, substituting the values,

$[MLT^{-2}]\neq[MLT^{-1}]$ hence it is not a dimensional homogeneous.

ii) $[MLT^{-2}]\neq [ML^2T^{-2}]$

Hence, it is not a dimensional homogeneous.

iii)

$[MLT^{-2}]= [ML^{-3}L^3LT^{-2}]=[MLT^{-2}]$

Hence, it is dimensional homogeneous equation.

iv)$[MLT^{-2}]\neq[M][LT^{-1}]$

Hence, the correct answer is option (iii)