Question

For the equation $F=A^a{v}^b{d}^c$, where $F$ is force, $A$ is area, $v$ is velocity and $d$ is density, the dimensional analysis give the following values for the exponents.

• A. a=1, b = 2, c =1
• B. a =2, b =1, c= 1
• C. a =1, b =1, c= 2
• D. a = 0, b =1, c = 1

Answer 1

The correct option is A a=1, b = 2, c =1

$F=A^a{v}^b{d}^c$

$M^1{L}^1{T}^{-2}=\left(L^2{)}^a\right(L{t}^{-1}{)}^b(M{L}^{-3}{)}^c$

$M^1{L}^1{T}^{-2}=L^{2a+b-3c}{T}^{-b}{M}^c$

$c=1$

$b=2$

$2a+b-3c=1$

$\Rightarrow a=1$

$\Rightarrow a=1,b=2,c=1$