A water drop breaks into 64 identical droplet | vedclass

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

Question

(D) Let $R$ be the radius of the large drop and $r$ be the radius of each small droplet. The surface area of each small droplet is $A_s = 4\pi r^2 = 1

Vedclass · Accepted Answer

$336 	imes 10^{-9} \,J$

Vedclass · Answer

(D) Let $R$ be the radius of the large drop and $r$ be the radius of each small droplet. The surface area of each small droplet is $A_s = 4\pi r^2 = 10^{-7} \,m^2$.Since the volume is conserved, $\frac{4}{3}\pi R^3 = 64 	imes \frac{4}{3}\pi r^3$, which gives $R^3 = 64r^3$, so $R = 4r$.The surface area of the large drop is $A_L = 4\pi R^2 = 4\pi (4r)^2 = 16(4\pi r^2) = 16 	imes 10^{-7} \,m^2$.The total surface area of $64$ droplets is $A_{total} = 64 	imes 10^{-7} \,m^2$.The increase in surface area is $\Delta A = A_{total} - A_L = (64 - 16) 	imes 10^{-7} = 48 	imes 10^{-7} \,m^2$.The increase in surface energy is $\Delta U = T 	imes \Delta A$, where $T = 0.07 \,N/m$.$\Delta U = 0.07 	imes 48 	imes 10^{-7} = 3.36 	imes 10^{-7} \,J = 336 	imes 10^{-9} \,J$.

$A$ water drop breaks into $64$ identical droplets, each with a surface area of $10^{-7} \,m^2$. If the surface tension of water is $0.07 \,N/m$, what is the increase in surface energy during this process?

Similar Questions

Energy required to form a soap bubble of diameter $20 \, cm$ will be (Surface tension for soap solution is $30 \, dynes/cm$)

Energy needed in breaking a liquid drop of radius $R$ into $n$ smaller drops,each of radius $r$,is [where $T$ is the surface tension of the liquid].

If $W_1$ is the work done in increasing the radius of a soap bubble from $r$ to $2r$ and $W_2$ is the work done in increasing the radius of the soap bubble from $2r$ to $3r$, then $W_1: W_2=$

$A$ mercury drop of radius $1 \ cm$ is divided into $10^6$ droplets of equal size. If the surface tension of mercury is $35 \times 10^{-3} \ N/m$,then the change in surface energy in the process is:

$A$ liquid drop having surface energy $E$ is sprayed into $512$ droplets of the same size. Then the final surface energy is

Vedclass Test Series

Exam Paper Generator

Online Exam Module