Why do bubbles rise in a soda water bottle?

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(B) When a soda bottle is opened,the pressure inside decreases,causing dissolved $CO_2$ gas to form bubbles. According to Archimedes' principle,any ob

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Due to the buoyant force being greater than the weight of the bubble.

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(B) When a soda bottle is opened,the pressure inside decreases,causing dissolved $CO_2$ gas to form bubbles. According to Archimedes' principle,any object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced by it. The buoyant force $(F_b)$ acting on the bubble is given by $F_b = V \rho_{liquid} g$,where $V$ is the volume of the bubble,$\rho_{liquid}$ is the density of the liquid,and $g$ is the acceleration due to gravity. The weight of the bubble $(W)$ is $W = V \rho_{gas} g$. Since the density of the gas $(\rho_{gas})$ is much smaller than the density of the liquid $(\rho_{liquid})$,the buoyant force is significantly greater than the weight of the bubble $(F_b > W)$. This net upward force causes the bubbles to accelerate and rise to the surface.

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