Two rain drops reach the earth with different | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The terminal velocity $v_T$ of a spherical drop is given by $v_T = \frac{2}{9} \frac{r^2 g (\rho - \sigma)}{\eta}$, where $r$ is the radius of the

Vedclass · Accepted Answer

$27:8$

Vedclass · Answer

(D) The terminal velocity $v_T$ of a spherical drop is given by $v_T = \frac{2}{9} \frac{r^2 g (\rho - \sigma)}{\eta}$, where $r$ is the radius of the drop.Thus, $v_T \propto r^2$.Given the ratio of terminal velocities is $\frac{v_{T_1}}{v_{T_2}} = \frac{9}{4}$.Since $\frac{v_{T_1}}{v_{T_2}} = \left(\frac{r_1}{r_2}\right)^2$, we have $\frac{r_1}{r_2} = \sqrt{\frac{9}{4}} = \frac{3}{2}$.The volume $V$ of a spherical drop is given by $V = \frac{4}{3} \pi r^3$, so $V \propto r^3$.The ratio of their volumes is $\frac{V_1}{V_2} = \left(\frac{r_1}{r_2}\right)^3 = \left(\frac{3}{2}\right)^3 = \frac{27}{8}$.

Two rain drops reach the earth with different terminal velocities having ratio $9:4$. Then the ratio of their volumes is

Similar Questions

If $f: R \rightarrow R$ is an even function having derivatives of all orders,then which of the following is an odd function?

If the direction ratios of two lines are given by $3lm - 4ln + mn = 0$ and $l + 2m + 3n = 0$, then the angle between the lines is:

$XOZ$-plane divides the line segment joining the points $(2, 3, 1)$ and $(6, 7, 1)$ in the ratio: (in $: 7$)

In a series $LCR$ circuit,what will be the nature of the circuit for frequencies higher than the resonance frequency?

When bauxite powder is mixed with coke and reacted with nitrogen at $2075 \ K$,carbon monoxide and $X$ are formed. What is the gas formed when $X$ is reacted with water?

Vedclass Test Series

Exam Paper Generator

Online Exam Module