Two satellites of equal mass are in circular orbits around earth. satellite a has a smaller orbital radius than satellite b. which statement is true regarding the kinetic energy , gravitational potential energy , and total mechanical energy =+=k+u of the satellites? g

Aparticle of mass m is projected with an initial velocity v0 in a direction making an angle α with the horizontal level ground as shown in the figure. the motion of the particle occurs under a uniform gravitational field g pointing downward. (a) write down the lagrangian of the system by using the cartesian coordinates (x, y). (b) is there any cyclic coordinate(s). if so, interpret it (them) physically. (c) find the euler-lagrange equations. find at least one constant of motion. (d) solve the differential equation in part (c) and obtain x and y coordinates of the projectile as a function of time. (e) construct the hamiltonian of the system, h, and write down the hamilton’s equations (canonical equations) of motion.

An object weighs 40n in air, weighs 20n when submerged in water and 30n when submerged in a liquid of unknown density. what is the density of the liquid?

Asmall electric heater, immersed in 80g of water in a calorimeter of 40j/k raises the temperature from 10.5 degree celsius to 25 degree celsius in 12 minutes. using the same apparatus with 50g of oil instead of water, it is found that the temperature of oil rises from 7 degree celsius to 27 degree celsius in 10 minutes. find specific heat capacity of the oil.