64 small drops of mercury, each of radius r and charge q coalesce to form a big drop. The ratio of the surface density of charge of each small drop with that of the big drop is

Question

64 small drops of mercury, each of radius r and charge q coalesce to form a big drop. The ratio of the surface density of charge of each small drop with that of the big drop is (A) 1: 64 (B) 64: 1 (C) 4: 1 (D) 1: 4

Tardigrade Admin · Accepted Answer

Here R3 = (4r)3 i.e. R = 4r (σ1/σ2) = (r2/4r2) = (1/4)

Q. $64$ small drops of mercury, each of radius $r$ and charge $q$ coalesce to form a big drop. The ratio of the surface density of charge of each small drop with that of the big drop is

1 : 64

64 : 1

4 : 1

1 : 4

Here $R^{3} = (4 r)^{3} i . e . R = 4 r$ $\frac{σ _{1}}{σ _{2}} = \frac{r ^{2}}{4 r ^{2}} = \frac{1}{4}$

Q. 64 small drops of mercury, each of radius r and charge q coalesce to form a big drop. The ratio of the surface density of charge of each small drop with that of the big drop is