64 small drops,each of radius r and charge q, | vedclass

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

Question

(D) Let $r$ be the radius and $q$ be the charge of each small drop. Let $R$ be the radius and $Q$ be the charge of the large drop.Since $64$ small dro

Vedclass · Accepted Answer

$1 : 4$

Vedclass · Answer

(D) Let $r$ be the radius and $q$ be the charge of each small drop. Let $R$ be the radius and $Q$ be the charge of the large drop.Since $64$ small drops coalesce to form one large drop,the total 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 total charge is also conserved: $Q = 64q$.The surface charge density $\sigma$ is defined as $\sigma = \frac{	ext{charge}}{	ext{area}} = \frac{q}{4\pi r^2}$.For the small drop,$\sigma_{small} = \frac{q}{4\pi r^2}$.For the large drop,$\sigma_{large} = \frac{Q}{4\pi R^2} = \frac{64q}{4\pi (4r)^2} = \frac{64q}{4\pi (16r^2)} = 4 	imes \frac{q}{4\pi r^2} = 4\sigma_{small}$.Therefore,the ratio of the surface charge density of a small drop to that of the large drop is $\frac{\sigma_{small}}{\sigma_{large}} = \frac{\sigma_{small}}{4\sigma_{small}} = \frac{1}{4}$.

$64$ small drops,each of radius $r$ and charge $q$,coalesce to form a single large drop. If the charge is conserved,what is the ratio of the surface charge density of a small drop to that of the large drop?

Similar Questions

The excess pressure inside a soap bubble is $1.5$ times the excess pressure inside a second soap bubble. The volume of the second bubble is '$x$' times the volume of the first bubble. The value of '$x$' is

The work done in breaking a drop of liquid of radius $R$ (Surface tension $T$) into $64$ equal drops is

$A$ spherical drop of water has a radius of $1\, mm$. If the surface tension of water is $70 \times 10^{-3} \, N/m$,then the difference of pressure between the inside and outside of the spherical drop is:

$216$ small identical liquid drops,each of surface area $A$,coalesce to form a bigger drop. If the surface tension of the liquid is $T$,what is the energy released in the process (in $AT$)?

The excess pressure inside a spherical soap bubble of radius $1 \,cm$ is balanced by a column of oil (specific gravity $= 0.8$), $2 \,mm$ high. The surface tension of the bubble is: (in $\,N/m$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module