Question

A soap bubble of radius 6 cm and another bubble of 8 cm coalesce under isothermal conditions in vacuum. The radius of the new bubble is:

• A. 3 cm
• B. 4 cm
• C. 10 cm
• D. 7 cm

Answer 1

The correct option is C 10 cm

Here, we have to use surface area conservation
so, surface area before coalesce is
$4\pi (6{)}^2+4\pi (8{)}^2$ -----------(1)
Surface area after coalesce is
$4\pi (R{)}^2$ ---------(2)
Equating both (1) and (2) we get
$4\pi (6{)}^2+4\pi (8{)}^2=4\pi (R{)}^2$
36 + 64 = $R^2$
10 = R
Hence, radius of new bubble is 10 cm