8 small drops,each of capacitance C,coalesce | vedclass

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

Question

(D) Let the radius of each small drop be $r$ and the radius of the large drop be $R$.Since the volume remains constant,the volume of $8$ small drops e

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(D) Let the radius of each small drop be $r$ and the radius of the large drop be $R$.Since the volume remains constant,the volume of $8$ small drops equals the volume of the large drop:$8 	imes (\frac{4}{3} \pi r^3) = \frac{4}{3} \pi R^3$$R^3 = 8r^3 \implies R = 2r$.The capacitance of a spherical drop is given by $C = 4 \pi \epsilon_0 r$.For the large drop,the capacitance $C' = 4 \pi \epsilon_0 R = 4 \pi \epsilon_0 (2r) = 2 	imes (4 \pi \epsilon_0 r) = 2C$.Therefore,the capacitance of the large drop is $2C$.

$8$ small drops,each of capacitance $C$,coalesce to form a single large drop. The capacitance of the large drop will be ........ $C$.

Similar Questions

The potentials of the two plates of a capacitor are $+10\,V$ and $-10\,V$. The charge on one of the plates is $40\,C$. The capacitance of the capacitor is........$F$.

What is the capacitance of a spherical conductor with a radius of $1 \ m$?

If the circumference of a sphere is $3 \ m$,then the capacitance of the sphere in water is (dielectric constant of water = $80$) (in $pF$)

The unit of permittivity of free space is

The capacitance of a spherical capacitor is $100 \ pF$. If the spacing between the two spheres is $1 \ cm$,then the radius of the inner sphere of the capacitor is: (in $cm$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module