Drops of an oil that has a mass density of \(700 \mathrm{~kg} / \mathrm{m}^{3}\) are released from a broken undersea oil pipe that is \(1000 \mathrm{~m}\) below the ocean surface.

(a) If the drops have an average diameter of \(100 \mu \mathrm{m}\), how long do they take to rise to the surface? The drops quickly reach terminal speed and experience a viscous drag force of magnitude \(F_{\text {wo }}^{\mathrm{d}}=(0.0200 \mathrm{~Pa} \cdot \mathrm{s}) R v\), where \(R\) is the radius of the drops and \(v\) is their speed.

(b) After a chemical dispersant is applied to the oil to reduce the average drop diameter to \(2.0 \mu \mathrm{m}\), how long do the drops take to rise to the surface? Use \(1000 \mathrm{~kg} / \mathrm{m}^{3}\) for the mass density of ocean water.