A liquid drop of diameter ‘D’ is split into 27 droplets. If T is surface tension of the liquid the change in energy is

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

$2 π D^{2} T$

$2 π D$

$2 π D^{2}$

Zero

answer is C.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

From the question volume is conserved,

Thus the initial volume is $\frac{4}{3} π {(\frac{D}{2})}^{2}$

final volume is $\frac{4}{3} {πr}^{2} 27$

By volume of conservation,

$\frac{4}{3} π {(\frac{D}{2})}^{2} = \frac{4}{3} {πr}^{2} \Rightarrow r = \frac{D}{6}$

Thus the initial energy = $4 π {(\frac{D}{2})}^{2} T$

final energy $= 4 π {(\frac{D}{6})}^{2} T \times 27$

Energy change = final energy - initial energy.

$= 4 π {(\frac{D}{6})}^{2} \times T \times 27 - 4 π {(\frac{D}{2})}^{2} \times T$

$= 4 {πTD}^{2} [\frac{27}{36} - \frac{1}{4}] = 4 {πTD}^{2} [\frac{18}{36}] = 2 {πTD}^{2}$

Hence the correct answer is $2 {πTD}^{2} .$

Watch 3-min video & get full concept clarity