n small spherical drops of the same size, eac | vedclass

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

Question

(D) Let $r$ be the radius of each small drop and $q$ be the charge on each small drop.The potential of a small drop is given by $V = \frac{kq}{r}$.Whe

Vedclass · Accepted Answer

$n^{2/3}V$

Vedclass · Answer

(D) Let $r$ be the radius of each small drop and $q$ be the charge on each small drop.The potential of a small drop is given by $V = \frac{kq}{r}$.When $n$ small drops coalesce to form a big drop of radius $R$ and charge $Q$, the total volume remains conserved.So, $n 	imes (\frac{4}{3}\pi r^3) = \frac{4}{3}\pi R^3$, which implies $R^3 = nr^3$ or $R = n^{1/3}r$.The total charge on the big drop is $Q = nq$.The potential of the big drop $V_{big}$ is given by $V_{big} = \frac{kQ}{R}$.Substituting the values of $Q$ and $R$, we get $V_{big} = \frac{k(nq)}{n^{1/3}r} = n^{1 - 1/3} 	imes \frac{kq}{r} = n^{2/3}V$.

$n$ small spherical drops of the same size, each charged to a potential $V$, coalesce to form a single big drop. The potential of the big drop is:

Similar Questions

What physical quantities may $X$ and $Y$ represent? ($Y$ represents the first mentioned quantity)

Three uncharged capacitors of capacitance $C_1$,$C_2$ and $C_3$ are connected as shown in the figure to one another and to points $A$,$B$ and $D$ at potentials $V_A$,$V_B$ and $V_D$. Then the potential at point $O$ will be

$n$ small drops, each of capacitance $C$, coalesce to form a single large drop. What is the ratio of the energy stored in the large drop to the energy stored in each small drop?

What are the charges stored in the $1 \,\mu F$ and $2 \,\mu F$ capacitors in the circuit below,once the currents become steady?

Each of the $N$ small drops has a radius $r$ and is charged to a potential $V$. If these drops coalesce to form a single large drop,what is the potential of the large drop?

Vedclass Test Series

Exam Paper Generator

Online Exam Module