A scuba diver at a depth of 20 m exhales,releasing a spherical bubble of gas with a diameter of 10 cm.The bubble floats towards the surface and assuming that it maintains its spherical shape,what is its diameter when it is 1.0 m below the surface?

Question

Quizplus · Accepted Answer

The pressure at a depth of 20 m is higher than at a depth of 1.0 m. As the bubble rises towards the surface, the pressure around it decreases and its volume increases. However, we are assuming that it maintains its spherical shape, which means that its radius must increase by a constant factor.

The pressure at a depth of 20 m is approximately 3 times higher than at a depth of 1.0 m (assuming that the density of water is constant). This means that the volume of the bubble should increase by a factor of 3 as it rises towards the surface.

The volume of a sphere is given by the formula: V = (4/3)πr^3. If the volume increases by a factor of 3, then the radius must increase by a factor of cube root of 3.

The diameter of the bubble at a depth of 1.0 m is therefore:

d = 2r = 2(10 cm) x cube root of 3 ≈ 14 cm.

Therefore, the best choice is D) 14 cm.

A Scuba Diver at a Depth of 20 M Exhales,releasing