You are handed a rod that is four times as dense on one side as it is on the other side, and two times as dense in the middle as it is on the least dense side. Further, you are told that the density varies quadratically. The mass of the rod is M and the length is L. Write your answers only in terms of these constants. (a) What is the moment of inertia about an axis that passes through the midpoint of the rod (and is perpendicular to the length of the rod)?
(b) What is the moment of inertia about an axis that passes through one of the ends of the rod (and is perpendicular to the length of the rod)?

What is the length x of the side of the triangle below? (hint: use the cosine function)

Na food processing facility, a spherical container of inner radius r1 5 40 cm, outer radius r2 5 41 cm, and ther- mal conductivity k 5 1.5 w/m · k is used to store hot water and to keep it at 100°c at all times. to accomplish this, the outer surface of the container is wrapped with a 800-w electric strip heater and then insulated. the temperature of the inner surface of the container is observed to be nearly 120°c at all times. as- suming 10 percent of the heat generated in the heater is lost through the insulation, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the container, (b) obtain a relation for the variation of temperature in the container material by solving the differential equation, and (c) evaluate the outer surface tempera- ture of the container. also determine how much water at 100°c this tank can supply steadily if the cold water enters at 20°c.

Which of the following is not an appropriate unit for acceleration? (kg/12 mihr? m/min/sec cm/30c?