What is the basic definition of a black hole?
a. any compact mass that emits no light
b. a dead star that has faded from view any object from which the escape velocity exceeds
c. the speed of light any object made from dark matter
d. a dead galactic nucleus that can only be viewed in infrared

In a hydrogen molecule there are a total of four charges, 2 protons in the two nuclei, and 2 electrons. how many unique charge-pairs are there (without double counting)?

Which of the following statement is false

The center of a long frictionless rod is pivoted at the origin, and the rod is forced to rotate in a vertical plane with constant angular velocity \omega. write down the lagrangian for a bead of mass m threaded on the rod, using r as your generalized coordinate, where r, \phi are the polar coordinates of the bead. (notice that \phi is not an independent variable since it is fixed by the rotation of the rod tobe \phi = \omega * t) solve lagrange's equation for r(t). what happens if the bead is initially at rest at the origin? if it is released from any point ro > 0, show that r(t) eventually grows exponentially. explain your results in terms of the centrifugal force m* \omega ^2 *r.