For the equation F propto Aa vb dc, 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

Question

For the equation F propto Aa vb dc, 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

Tardigrade Admin · Accepted Answer

As,[M L T-2]=[L2 a][Lb T-b][Mc L-3 c]=[Mc L2 a+c-3 c T-b] 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 ⇒ 2 a =2 or a=1

Q. 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

1, 2, 1

2, 1, 1

1, 1, 2

0, 1, 1

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

Q. For the equation F∝Aavbdc, 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