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

Question

27 identical drops of mercury are charged simultaneously with the same potential of 10 Volt. Assuming the drop to be spherical, if all the charged drops are made to combine to form one large drop, then its potential will be Volt (A) 45 units (B) 135 units (C) 270 units (D) 90 units.

Tardigrade Admin · Accepted Answer

Let the charge on one smaller drop be q. Potential at each small drop

V = \frac{K q}{r}

where

r

is the radius of each small drop and

V

is 10 volts.

∴ 10 = \frac{K q}{r}

We get

q = \frac{10 r}{K}

Let radius of bigger drop be

R

. Volume of 27 small drops is equal to volume of one bigger drop.

∴ \frac{4 π}{3} R^{3} = 27 \times \frac{4 π}{3} r^{3}

⟹ R = 3 r

Total charge on bigger drop

Q = 27 q = \frac{270 r}{K}

Potential of bigger drop

V_{b} = \frac{K Q}{R}

⟹ V_{b} = \frac{K \times \frac{270 r}{K}}{3 r} = 90 V o lt s

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

45 units

135 units

270 units

90 units.