Excess pressure of one soap bubble is four times more than the other. Then the ratio of volume of first bubble to another one i

The correct option is 1:64.

Let us find the ratio of the volume of the first soap bubble to the second soap bubble step-by-step.

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

From this formula, we can see that the excess pressure $P$ is inversely proportional to the radius $R$ of the bubble:
$P\propto \frac{1}{R}$
Therefore, the ratio of the excess pressures of two bubbles is:
$\frac{P_1}{P_2}$

The problem states that the excess pressure of the first soap bubble is four times that of the other bubble:
$P_1=4P_2$
This gives the ratio of their pressures as:
$\frac{P_1}{P_2}$

Substituting this pressure ratio into our relation for the radii, we get:
$\frac{R_2}{R_1}$
Which means:
$\frac{R_1}{R_2}$

The volume $V$ of a spherical soap bubble of radius $R$ is given by:
$V=\frac{4}{3}\pi R^3$
Thus, the volume is directly proportional to the cube of the radius:
$V\propto R^3$

The ratio of the volume of the first bubble to the second bubble is:
$\frac{V_1}{V_2}$

Substituting the value of the radius ratio $\frac{R_1}{R_2}$ into this equation:
$\frac{V_1}{V_2}$

Thus, the ratio of the volume of the first bubble to that of the second bubble is 1:64.