We can solve for the critical density of the universe using the same method we used for finding the escape velocity. let's take an arbitrary point p in the universe, and consider a spherical shell of radius r0 around that point. according to hubble's law, an observer at point p will see a galaxy at point q on that spherical shell receding at velocity v=h0r0. what is the kinetic energy k of a galaxy of mass m at point q, relative to point p? express your answer in terms of h0, r0, and m. k =

Acyclotron is used to produce a beam of high-energy deuterons that then collide with a target to produce radioactive isotopes for a medical procedure. deuterons are nuclei of deuterium, an isotope of hydrogen, consisting of one neutron and one proton, with total mass 3.34×10−27kg. the deuterons exit the cyclotron with a kinetic energy of 6.40 mev .a-what is the speed of the deuterons when they exit? b-if the magnetic field inside the cyclotron is 1.25 t, what is the diameter of the deuterons' largest orbit, just before they exit? c-if the beam current is 350 μa how many deuterons strike the target each second?