Which of the following is dimensionless?

Options

A. `(v^(2))/(rg)`
B. `(v^(2)g)/v`
C. `(vg)/r`
D. `v^(2)rg`

Answer

A

Explanation

(i) `(v^(2))/(rg)=([LT^(-1)]^(2))/([L][LT^(-2)])," "(v^(2))/(rg)` is dimensionless
(ii) `(v^(2)g)/r=([LT^(-1)]^(2)[LT^(-2)])/([L])=L^(2)T^(-4)`
(iii) `(vg)/r=([LT^(-1)][LT^(-2)])/([L])=LT^(-3)`
(iv) `v^(2)rg=[LT^(-1)][L][LT^(-2)]=L^(4)T^(-4)`