Question

Under isothermal conditions, two soap bubbles of radii 'r₁' and 'r₂' coalesce to form a big drop. The radius of the big drop is ______.

Options

• `(r_1-r_2)^(1/2)`

• `(r_1+r_2)^(1/2)`

• `(r_1^2+r_2^2)^(1/2)`

• `(r_1^2-r_2^2)^(1/2)`

Answer 1

Under isothermal conditions, two soap bubbles of radii 'r₁' and 'r₂' coalesce to form a big drop. The radius of the big drop is `underline((r_1^2+r_2^2)^(1/2))`.

Explanation:

Under isothermal conditions, the surface tension remains constant. If r is the radius of the digger drop, then

Final surface energy = Initial surface energy

`therefore8pi^2T=8pi_1^2T+8pi_2^2T`

`thereforer^2=r_1^2+r_2^2`

`thereforer=(r_1^2+r_2^2)^(1/2)`