Final answer:
Using the formula P = σ/r for the pressure inside a spherical object, the effective surface tension of a balloon with a 10.0-cm radius and a 1.50 cm of water gauge pressure is calculated to be 14.71 N/m, none of the provided answer choices match this result.
Step-by-step explanation:
To find the effective surface tension of the balloon, we can use the formula for the pressure inside a spherical bubble, given by P = 2σ/r, where P is the pressure, σ is the surface tension, and r is the radius. For a rubber balloon with a 10.0-cm radius and a gauge pressure of 1.50 cm of water (≈ 147.1 Pa), the equation equates to σ = Pr/2. By inserting our known values into the equation, we get:
σ = (147.1 Pa)(0.10 m) / 2 = 7.355 N/m
However, since this balloon does not form a thin film like a soap bubble but rather has a single interface, we must consider only one surface layer, thus the pressure inside a spherical object is P = σ/r, and the corresponding surface tension will be σ = Pr. Using this formula, we get:
σ = (147.1 Pa)(0.10 m) = 14.71 N/m
This answer is not exactly matching any of the provided options (a) 1.38 N/m (b) 1.74 N/m (c) 2.20 N/m (d) 2.56 N/m. It is possible that there was a mistake in the provided question's options or in its interpretation for the calculation.