Question

A water drop of radius 1 cm is broken into 729 equal droplets. If surface tension of water is 75 dyne/cm, then the gain in surface energy upto first decimal place will be :
(Given $\pi$ = 3.14)

• A. $8.5 × 10^{–4} J$
• B. $8.2 × 10^{–4} J$
• C. $7.5 × 10^{–4} J$
• D. $5.3 × 10^{–4} J$

Answer 1

Answer: (C)

$7.5 × 10^{–4} J$

Answer 2

$729×\frac 43\pi r^3=\frac 43\pi R^3$
$R = 9r$ ……(1)
Then, the gain in surface energy
$ΔU = S × ΔA$ …..(2)
$△U=S×{−4\pi R^2+729×4\pi r^2}$
$△U=S×4π(729r^2–81r^2)$
$△U=7.5×10^{−4}J$

So, the correct option is (C): $7.5 × 10^{–4} J$