A ball of mass m and radius R is both sliding and spinning on a horizontal surface so that its rotational kinetic energy equals its translational kinetic energy. What is the ratio of the ball’s center-ofmass speed to the speed due to rotation only of a point on the ball’s surface? The moment of inertia of the ball is 0.63 m R2 .

What would the difference of spectral lines emitted by hydrogen gas in distant galaxies which is normally found at a wavelength of 21 cm on earth, be observed at 21.1 centimeters?

Consider the particle-in-a-box problem in 1d. a particle with mass m is confined to move freely between two hard walls situated at x = 0 and x = l. the potential energy function is given as (a) describe the boundary conditions that must be satisfied by the wavefunctions ψ(x) (such as energy eigenfunctions). (b) solve the schr¨odinger’s equation and by using the boundary conditions of part (a) find all energy eigenfunctions, ψn(x), and the corresponding energies, en. (c) what are the allowed values of the quantum number n above? how did you decide on that? (d) what is the de broglie wavelength for the ground state? (e) sketch a plot of the lowest 3 levels’ wavefunctions (ψn(x) vs x). don’t forget to mark the positions of the walls on the graphs. (f) in a transition between the energy levels above, which transition produces the longest wavelength λ for the emitted photon? what is the corresponding wavele

The charge on a charged sphere is: a)concentrated at its centerb)distributed uniformly throughout its volumec)clustered on its centerd)distributed uniformly over its surface