Asize-5 soccer ball of diameter 22.6 cm and mass 426 g rolls up a hill without slipping, reaching a maximum height of 5.00 m above the base of the hill. we can model this ball as a thin-walled hollow sphere. (a) at what rate was it rotating at the base of the hill

Uranium has two naturally occurring isotopes. 238u has a natural abundance of 99.3% and 235u has an abundance of 0.7%. it is the rarer 235u that is needed for nuclear reactors. the isotopes are separated by forming uranium hexafluoride uf6, which is a gas, then allowing it to diffuse through a series of porous membranes. 235uf6 has a slightly larger rms speed than 238uf6 and diffuses slightly faster. many repetitions of this procedure gradually separate the two isotopes. what is the ratio of the rms speed of 235uf6 to that of 238uf6? express your answer to five significant figures.

People with normal vision cannot focus their eyes underwater if they aren't wearing a face mask or goggles and there is water in contact with their eyes. in a simplified model of the human eye, the aqueous and vitreous humors and the lens all have a refractive index of 1.40, and all the refraction occurs at the cornea, whose vertex is 2.60 cm from the retina.with the simplified model of the eye, what corrective lens (specified by focal length as measured in air) would be needed to enable a person underwater to focus an infinitely distant object? (be careful-the focal length of a lens underwater is not the same as in air! assume that the corrective lens has a refractive index of 1.62 and that the lens is used in eyeglasses, not goggles, so there is water on both sides of the lens. assume that the eyeglasses are 2.05cm in front of the eye.)

What do we mean by the event horizon of a black hole?