Question

For the equation $F \propto A^{a} v^{b} d^{c}$, 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)

As,$\left[M L T^{-2}\right]=\left[L^{2 a}\right]\left[L^{b} T^{-b}\right]\left[M^{c} L^{-3 c}\right]=\left[M^{c} L^{2 a+c-3 c} T^{-b}\right]$
Comparing powers of $M, L$ and $T$, we get
$c=1,\,2 a+b-3 c =1,\,-b=-2$ or $b=2$
$2 a+2-3(1) =1$
$\Rightarrow 2 a =2$
or $a=1$