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9.2 , surface tension — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics9.2 , surface tension1 Mark
MCQ
A soap bubble of radius $3\, {cm}$ is formed inside the another soap bubble of radius $6\, {cm}$. The radius of an equivalent soap bubble which has the same excess pressure as inside the smaller bubble with respect to the atmospheric pressure is .......... ${cm}$ 
  • A
    $5$
  • B
    $4$
  • ✓
    $2$
  • D
    $3$
✓

Answer

Correct option: C.
$2$
c
Excess pressure inside the smaller soap bubble

$\Delta {P}=\frac{4 {S}}{{r}_{1}}+\frac{4 {S}}{{r}_{2}}\ldots \text { (i) }$

The excess pressure inside the equivalent soap bubble

$\Delta {P}=\frac{4 {S}}{{R}_{{eq}}} \ldots \text { (ii) }$

From $ (i) \,\& \,(ii)$

$\frac{4 {S}}{{R}_{{eq}}}=\frac{4 {S}}{{T}_{1}}+\frac{4 {S}}{{T}_{2}}$

$\frac{1}{{R}_{{eq}}}=\frac{1}{{T}_{1}}+\frac{1}{{I}_{2}}$

$=\frac{1}{6}+\frac{1}{3}$

${R}_{{eq}}=2 \,{cm}$

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