# What is the change in surface energy, when a mercury drop of radius R splits up into 1000 droplets of radius r? Option 1) $8\rho R^{2}T$ Option 2) $16 \rho R^{2}T$ Option 3) $24 \rho R^{2}T$ Option 4) $36 \rho R^{2}T$

As we discussed in concept

Surface Energy -

It is defined as the amount of work done in increasing the area of the liquid against surface tension.

-

$n\frac{4}{3}\pi r^{3}=\frac{4}{3}\pi R^{3}$

$nr^{3}=R^{3}$

$=> R=n^{1/3}r$

where n= 10000

After calculeting we get $r=36\rho R^2T$

Option 1)

$8\rho R^{2}T$

Option is incorrect

Option 2)

$16 \rho R^{2}T$

Option is incorrect

Option 3)

$24 \rho R^{2}T$

Option is incorrect

Option 4)

$36 \rho R^{2}T$

Option is correct

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