Question

two rain drops of radii 0.5mm and 1.0mm are falling on a metallic plate.The ratio of the velocities of these drops are

Answer 1

the ratio velocities are 5:1

Answer 2

Answer:

The ratio of the velocities of these drops are 1:4

Explanation:

Given that,

Radius of first rain drop = 0.5 mm

Radius of second rain drop = 1.0 mm

We know that,

The formula of terminal velocity is defined as:

$V_{t}=\dfrac{2}{9}\times\dfrac{r^2(\rho-\sigma)g}{\eta}$

Where, $\eta$ = coefficient of viscosity

The terminal velocity for first rain drop

$V_{t}=\dfrac{2}{9}\times\dfrac{(0.5)^2(\rho-\sigma)g}{\eta}$

The terminal velocity for second rain drop

$V'_{t}=\dfrac{2}{9}\times\dfrac{(1.0)^2(\rho-\sigma)g}{\eta}$

The ratio of the velocities of these drops are

$\dfrac{V_{t}}{V'_{t}}=\dfrac{\dfrac{2}{9}\times\dfrac{(0.5)^2(\rho-\sigma)g}{\eta}}{\dfrac{2}{9}\times\dfrac{(1.0)^2(\rho-\sigma)g}{\eta}}$

$\dfrac{V_{t}}{V'_{t}}=\dfrac{(0.5)^2}{(1.0)^2}$

$\dfrac{V_{t}}{V'_{t}}=\dfrac{1}{4}$

Hence, The ratio of the velocities of these drops are 1:4