Question

Eight similar drops of mercury are maintained at 12 V each. All these spherical drops combine into a single big drop. The potential energy of bigger drop will be ______ E. Where E is the potential energy of a single smaller drop.

Options

• 31

• 32

• 33

• 34

Answer 1

Eight similar drops of mercury are maintained at 12 V each. All these spherical drops combine into a single big drop. The potential energy of bigger drop will be 32 E. Where E is the potential energy of a single smaller drop.

Explanation:

from law of conservation of charge

q_i = q_f  ⇒ 8 × (4πE₀R) × 12 = (4πER¹) × V_f

⇒ 96 R = V_fR¹     ...(i)

And, `8xx4/3pi"R"^3= 4/3pi"R"^1 3`

8 = `("R"^1/"R")^3`

R¹ = 2R      ...(ii)

From (i) & (ii), we get

So, 96 R = V_f × 2R ⇒ V_f = 48 Volt

V_f = `1/2"C"_"f""V"_"f"^2`

= `1/2xx(4piepsilon_0"R"^1)"V"_"f"^2`

= `1/2xx(4piepsilon_0xx2"R")xx48^2`

= `(1/2xx4piepsilon_0"R"xx12^2)xx(48^2xx2)/12^2`

= 32 E