If the radius of a soap bubble is four times that of another, then the ratio of their excess pressures will be

The correct option is 1:4.

Step-by-step explanation:

The excess pressure inside a soap bubble is given by the formula:
$P=\frac{4T}{R}$
where:
• $P$ is the excess pressure,
• $T$ is the surface tension of the soap solution, and
• $R$ is the radius of the soap bubble.

Since the surface tension ($T$) is constant for both soap bubbles, the excess pressure is inversely proportional to the radius of the bubble:
$P\propto \frac{1}{R}$

Let $R_1$ and $R_2$ be the radii of the two soap bubbles, and $P_1$ and $P_2$ be their respective excess pressures.

According to the question, the radius of the first bubble is four times that of the second bubble:
$R_1=4R_2$

Now, let's find the ratio of their excess pressures:
$\frac{P_1}{P_2}=\frac{R_2}{R_1}$

Substitute $R_1=4R_2$ into the equation:

Simplifying the ratio:
$\frac{P_1}{P_2}=\frac{1}{4}$

Therefore, the ratio of their excess pressures is 1:4.