Mechanical Properties Of Fluids Question 2
Question 2 - 25 January - Shift 2
A spherical drop of liquid splits into 1000 identical spherical drops. If $u_i$ is the surface energy of the original drop and $u_f$ is the total surface energy of the resulting drops, the (ignoring evaporation). $\frac{u_f}{u_i}=(\frac{10}{x})$. Then value of $x$ is
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Answer: (1)
Solution:
Formula: Surface Tension
Surface Tension $=T$
$R$ : Radius of bigger drop
$r$ : Radius of smaller drop
Volume will remain same
$\frac{4}{3} \pi R^{3}=1000 \times \frac{4}{3} \pi r^{3}$
$R=10 r$
$u_i=T .4 \pi R^{2}$
$u_f=T .4 \pi r^{2} \times 1000$
$\frac{u_f}{u_i}=\frac{1000 r^{2}}{R^{2}}$
$\frac{u_f}{u_i}=\frac{10}{1}$
So, $x=1$
