Two soap bubbles of radii 3 cm and 4 cm coalesce under isothermal conditions in vacuum to form a single bubble of radius r 1. If the two same soap bubbles coalesce in atmosphere, they form a single bubble with radius of interface r2. Find (r2/r1).

Question

Two soap bubbles of radii 3 cm and 4 cm coalesce under isothermal conditions in vacuum to form a single bubble of radius r 1. If the two same soap bubbles coalesce in atmosphere, they form a single bubble with radius of interface r2. Find (r2/r1). (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

In vacuum under isothermal conditions, radius of drop formed,

r_{1} = r_{A}^{2} + r_{B}^{2} = 3^{2} + 4^{2} = 5 c m

Under atmospheric condition, radius of interface of drop formed

r_{2} = \frac{r _{A} r _{B}}{r _{B} - r _{A}} = \frac{3 \times 4}{4 - 3}

= 12 c m

∴ \frac{r _{2}}{r _{1}} = \frac{12}{5} = 2.4

Q. Two soap bubbles of radii 3cm and 4cm coalesce under isothermal conditions in vacuum to form a single bubble of radius r1​. If the two same soap bubbles coalesce in atmosphere, they form a single bubble with radius of interface r2​. Find r1​r2​​.

In vacuum under isothermal conditions, radius of drop formed, r1​=rA2​+rB2​​=32+42​=5cm Under atmospheric condition, radius of interface of drop formed r2​=rB​−rA​rA​rB​​=4−33×4​ =12cm ∴r1​r2​​=512​=2.4

Q. Two soap bubbles of radii $3 c m$ and $4 c m$ coalesce under isothermal conditions in vacuum to form a single bubble of radius $r_{1}$ . If the two same soap bubbles coalesce in atmosphere, they form a single bubble with radius of interface $r_{2}$ . Find $\frac{r _{2}}{r _{1}}$ .