A soap bubble, having radius of 1 ; mm, is blown from a detergent… - Vidyadip

MCQ

A soap bubble, having radius of $1\; \mathrm{mm}$, is blown from a detergent solution having a surface tension of $2.5 \times 10^{-2}\; N / m$. The pressure inside the bubble equals at a point $Z_{0}$ below the free surface of water in a container. Taking $g=10\; \mathrm{m} / \mathrm{s}^{2}$ density of water $=10^{3} \;\mathrm{kg} / \mathrm{m}^{3},$ the value of $\mathrm{Z}_{0}$ is......$cm$

A
$100$
B
$10$
✓
$1$
D
$0.5 $

✓

Answer

Correct option: C.

$1$

c
$P=P_{0}+\rho g Z_{0}\ldots(i)$

Also, $\mathrm{P}=\mathrm{P}_{0}+\frac{4 \mathrm{T}}{\mathrm{R}}\ldots$ (ii)

From $(i) \;and\; (ii)$

$\rho g Z_{0}=\frac{4 \mathrm{T}}{\mathrm{R}}$

$\mathrm{z}_{0}=\frac{4 \mathrm{T}}{\mathrm{pgR}}$

$=\frac{4 \times 2.5 \times 10^{-2}}{10^{3} \times 10 \times 10^{-3}}=10^{-2} \mathrm{m}=1 \;\mathrm{cm}$

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