Two rain drops of same radius are falling thr | vedclass

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

Question

(D) The terminal velocity $v$ of a spherical drop falling through a viscous medium is given by $v = \frac{2r^2(\rho - \sigma)g}{9\eta}$.Thus,$v \propt

Vedclass · Accepted Answer

$5 	imes 4^{1/3} \,cm/s$

Vedclass · Answer

(D) The terminal velocity $v$ of a spherical drop falling through a viscous medium is given by $v = \frac{2r^2(ho - \sigma)g}{9\eta}$.Thus,$v \propto r^2$.Let the radius of each small drop be $r$ and the radius of the big drop be $R$.Since the volume is conserved when the two drops coalesce,$\frac{4}{3}\pi R^3 = 2 	imes \frac{4}{3}\pi r^3$,which implies $R^3 = 2r^3$ or $R = 2^{1/3}r$.Given the initial terminal velocity $v_1 = 5 \,cm/s$,the new terminal velocity $v_2$ is:$v_2 = v_1 	imes \left(\frac{R}{r}ight)^2$$v_2 = 5 	imes \left(\frac{2^{1/3}r}{r}ight)^2$$v_2 = 5 	imes (2^{1/3})^2 = 5 	imes 2^{2/3} = 5 	imes 4^{1/3} \,cm/s$.

Two rain drops of same radius are falling through air each with a steady speed of $5 \,cm/s$. If the drops coalesce,the new steady velocity of the big drop will be

Similar Questions

$A$ metal sphere of radius $R$,density $\rho_1$ moves with terminal velocity $V_1$ through a liquid of density $\sigma$. Another sphere of same radius but density $\rho_2$ moves through the same liquid. Its terminal velocity is $V_2$. The ratio $V_1: V_2$ is

The velocity of a small spherical ball of mass $m$ and density $d_1$,when dropped in a container filled with glycerine,becomes constant after some time. The viscous force acting on the ball if the density of glycerine is $d_2$ is

We have three beakers $A, B$,and $C$ containing glycerine,water,and kerosene respectively. They are stirred vigorously and placed on a table. The liquid which comes to rest at the earliest is

$A$ sphere of mass $M$ and radius $R$ is falling in a viscous fluid. The terminal velocity attained by the falling object will be proportional to

$A$ solid ball of volume $V$ is dropped in a viscous liquid. It experiences a viscous force $F$. If a solid ball of volume $2V$ of the same material is dropped in the same fluid,then the viscous force acting on it will be

Vedclass Test Series

Exam Paper Generator

Online Exam Module