Tamsen and vera imagine visiting another planet, planet x, whose gravitational acceleration, gx, is different from that of earth's. they envision a pendulum, whose period on earth is 2.243 s, that is set in motion on planet x, and the period is measured to be 1.510 s. what is the ratio of gx/gearth? neglect any effects caused by air resistance. (gx/ge= if the average density of planet x is equal to earthes average density, pe, what is the ratio of rx/re, where re is the mean radius of earth? (assume both planets are spherical. recall that p= m/v and vsphere= 4/3 pi r^3.) (rx/re= ? )

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.

At time t=0, a particle is located at the point (3,6,9). it travels in a straight line to the point (5,2,7), has speed 8 at (3,6,9) and constant acceleration 2i−4j−2k. find an equation for the position vector of the particle.

Charge is distributed along the entire x-axis with uniform density λ. how much work does the electric field of this charge distribution do on an electron that moves along the y-axis from y = a to y = b? (use the following as necessary: a, b, ε0, λ, and q for the charge on an electron.)