Question

A soap bubble in vacuum has a radius $3cm$ and another soap bubble in vacuum has radius $4cm$. If two bubbles coalesce under isothermal condition. Then the radius of the new bubble will be

• A. $7cm$
• B. $5cm$
• C. $4.5cm$
• D. $2.3cm$

Answer 1

The correct option is B $5cm$

If $r_1$ $r_2$ be radius of soap bubbles before and after the coalesce $p_1,p_{2}andp$ the pressure then, applying gas laws equation

$p_1{V}_1+p_2{V}_2=pV$

$\frac{4T}{r_1}\times \frac{4}{3}\pi r_1^3+\frac{4T}{r_2}\times \frac{4}{3}\pi r_2^3=\frac{4T}{r}\times \frac{4}{3}\pi r^3$

$r_1^2+r_2^2=r^2$

$r^2=4^2+3^2$

$r=5cm$