Question

The resistive force on a very-high-velocity object of area A passing through a gas of density ρ at a velocity v is

Force$\sim A^{r}\rho^{s}v^{t}$ Then –

• A. $\text{r } = \text{ 2, s } = \text{ 1, t } = \text{ 1}$
• B. $\text{r } = \text{ 2, s } = \text{ 1, t } = \text{ 2}$
• C. $\text{r } = \text{ 1, s } = \text{ 1, t } = \text{ 2}$
• D. $\text{r } = \text{ 1, s } = \text{ 1, t } = \text{ 1}$

Answer 1

Answer: (C)

$\text{r } = \text{ 1, s } = \text{ 1, t } = \text{ 2}$

Answer 2

[F] = [A]^r [ρ]^s [v]^t

MLT^–2 = L^2r M^s L^–3s L^tT^–t = L^2r+t–3s M^s T^–t

equating the powers of each dimension give

2r + t – 3s = 1, s = 1, t = 2

i.e., r = 1; s = 1; t = 2