The excess pressure inside a spherical drop of water is three times that of another drop of water. The ratio…

The excess pressure inside a spherical drop of water is three times that of another drop of water. The ratio of their surface area is
  1. $3: 1$
  2. $6: 1$
  3. $1: 9$
  4. $1: 3$

Solution

Excess pressure $p=\frac{2 T}{r}$ $\frac{p_{1}}{p_{2}}=\frac{r_{2}}{r_{1}}=3$ $\begin{array}{l} \therefore r_{2}=3 r_{1} \\ \frac{A_{1}}{A_{2}}=\frac{\pi r_{1}^{2}}{\pi r_{2}^{2}}=\left(\frac{r_{1}}{r_{2}}\right)^{2}=\frac{1}{(3)^{2}}=\frac{1}{9} \end{array}$ .

Asked in: MHT CET 2020 (13 Oct Shift 2)

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