Question

For the equation $F = A^av^bd^c$ , where $F$ is the force, $A$ is the area, $v$ is the velocity and $d$ is the density, the values of $a, b$ and $c$ are respectively

• A. 1, 2 ,1
• B. 2, 1, 1
• C. 1, 1, 2
• D. 0, 1, 1

Answer 1

Answer: (A)

$F=A^{a} v^{b} d^{c}$
$M^{1} L^{1} T^{-2}=\left(L^{2}\right)^{a}\left(L t^{-1}\right)^{b}\left(M L^{-3}\right)^{c}$
$M^{1} L^{1} T^{-2}=L^{2 a+b-3 c} T^{-b} M^{c}$
$c=1$
$b=2$
$2 a+b-3 c=1$
$\Rightarrow a=1$
$\Rightarrow a=1, b=2, c=1$