Asphere of polymer of radius r contains an initial amount m_0 of dissolved drug that is uniformly distributed within the sphere initially. if diffusion within the polymer controls the rate of release of the drug to the surrounding environment, then the fractional amount released as a function of time may be written as: m/m_0 = 1 - 6/pi^2 exp (-pi^2 d t/r^2) for 0.5 lessthanorequalto m/m_0 lessthanorequalto 1. a) find an expression for the half-time (i. e. the time at which half of the drug has been released. b) find an expression for the rate of release (dm/dt) at the half-time. this is often used as a nominal measure of the performance of a delivery system. c) what is the characteristic time scale for diffusion in this system? how does the half-time that you calculated in part (a) compare with the estimated characteristic time? is the system in a particular time-dependent limit that we discussed in class, or not necessarily?

i had the same answer and put c. deflect randomly in multiple directions.   i looked it up on google and what i found was this;

scattering of light: by small particles and molecules in the atmosphere. different from reflection, where radiation is deflected in one direction, some particles and molecules found in the atmosphere have the ability to scatter solar radiation in all directions.

i know it's kinda annoying when you are just given a google article but this is why i think it is c.   i will try to let you know if i got it right.

the correct answer to the question is it has inertia.

explanation:

the splashing of water in the bottle can be explained in terms of inertia of motion.

from newton's first law of motion, we know that a body moving with uniform velocity along a straight line will keep on moving with the same velocity along that line unless and until it is compelled by some external unbalanced force. it is known as inertia of motion.

as per the question, the passenger is in the moving car. the open water bottle has the same velocity as that of passenger as he is holding the bottle.

when the car stops, the passenger will move in forward direction due to the inertia of motion. same also happens in case of water present in the bottle. the water splashed out as its inertia of motion is destroyed .