27 identical drops of mercury are charged sim | vedclass

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

Question

(A) Let the radius of each small drop be $r$ and the charge on each be $q$. The potential of a small drop is given by $V = \frac{kq}{r} = 10 \ V$.When

Vedclass · Accepted Answer

$90$

Vedclass · Answer

(A) Let the radius of each small drop be $r$ and the charge on each be $q$. The potential of a small drop is given by $V = \frac{kq}{r} = 10 \ V$.When $n = 27$ drops combine to form a large drop of radius $R$,the volume remains conserved: $\frac{4}{3}\pi R^3 = n \cdot \frac{4}{3}\pi r^3$,which implies $R = n^{1/3}r$.For $n = 27$,$R = (27)^{1/3}r = 3r$.The total charge on the large drop is $Q = nq = 27q$.The potential of the large drop is $V^{\prime} = \frac{kQ}{R} = \frac{k(nq)}{n^{1/3}r} = n^{2/3} \left(\frac{kq}{r}ight) = n^{2/3}V$.Substituting the values: $V^{\prime} = (27)^{2/3} 	imes 10 = (3^3)^{2/3} 	imes 10 = 3^2 	imes 10 = 9 	imes 10 = 90 \ V$.

$27$ identical drops of mercury are charged simultaneously with the same potential of $10 \ V$. Assuming the drops to be spherical,if all the charged drops are made to combine to form one large drop,then its potential will be . . . . . . volt.

Similar Questions

$1000$ small drops,each of radius $r$ and charge $q$,coalesce to form a single large drop. How many times greater is the potential of the large drop compared to the potential of a small drop?

Four equal capacitors are connected to a $10 \, V$ battery as shown in the figure. The potentials of $A$ and $B$ are:

Two capacitors of $2 \mu F$ and $3 \mu F$ are charged to $150 \ V$ and $120 \ V$ respectively. The plates of the capacitors are connected as shown in the figure. $A$ discharged capacitor of capacity $1.5 \mu F$ is connected to the free ends of the wire. Then:

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

$A$ capacitor of capacity $C$ is connected to a battery of potential $V$ in parallel. The distance between its plates is reduced to half at once,while the battery remains connected. Then,the energy supplied by the battery to charge the capacitor to potential $V$ again is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module