Question

Two soap bubbles of radius 2 cm and 4 cm, respectively, are in contact with each other. The radius of curvature of the common surface, in cm, is _______________.

Hint:

The radius of curvature of the common surface of two soap bubbles in contact is calculated using the formula \( r = \frac{r_1 \cdot r_2}{r_1 - r_2} \).

Answer 1

Correct Answer: 4

For two soap bubbles in contact, the radius of curvature \( r \) of the common surface is given by: \[ r = \frac{r_1 \cdot r_2}{r_1 - r_2} \] where \( r_1 = 4 \, \text{cm} \) and \( r_2 = 2 \, \text{cm} \): \[ r = \frac{2 \times 4}{4 - 2} = \frac{8}{2} = 4 \, \text{cm} \] Thus, the answer is \( \boxed{4} \).