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

Question

Two rain drops reach the earth with different terminal velocities having ratio 9: 4. Then the ratio of their volumes is (A) 3: 2 (B) 4: 9 (C) 9: 4 (D) 27: 8

Tardigrade Admin · Accepted Answer

Terminal velocity, vT propto r2 or (vT1/vT2)=(r12/r22) ∴ √(9/4)=(r1/r2) or (r1/r2)=(3/2) ∴ v=(4/3) π r3 or (v1/v2)=(r13/r23) =(27/8)

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

3: 2

4: 9

9: 4

27: 8

Terminal velocity, $v_{T} \propto r^{2}$
or $\frac{v _{T_{1}}}{v _{T_{2}}} = \frac{r _{1}^{2}}{r _{2}^{2}}$
$∴ \frac{9}{4} = \frac{r _{1}}{r _{2}}$
or $\frac{r _{1}}{r _{2}} = \frac{3}{2}$
$∴ v = \frac{4}{3} π r^{3}$
or $\frac{v _{1}}{v _{2}} = \frac{r _{1}^{3}}{r _{2}^{3}}$
$= \frac{27}{8}$

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