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

Question

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 (A) 1, 2 ,1 (B) 2, 1, 1 (C) 1, 1, 2 (D) 0, 1, 1

Tardigrade Admin · Accepted Answer

F=Aa vb dc M1 L1 T-2=(L2)a(L t-1)b(M L-3)c M1 L1 T-2=L2 a+b-3 c T-b Mc c=1 b=2 2 a+b-3 c=1 ⇒ a=1 ⇒ a=1, b=2, c=1

Q. For the equation $F = A^{a} v^{b} d^{c}$ , 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

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

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