Use equation (2.190) to show that the razor-thin disk for which the circular speed is given by (2.262a) has surface density (toomre 1963) 1 σ(r ) (2.262b) v1 a2/r2 2tgr show that these formulae correspond to the mestel disk in an appropriate limit. show that the surface density (2.68b) of the kuzmin disk is obtained when £(r) is differentiated with respect to a2, and hence recover the circular speed of this model

Aball is thrown upward. at a height of 10 meters above the ground, the ball has a potential energy of 50 joules (with the potential energy equal to zero at ground level) and is moving upward with a kinetic energy of 50 joules. what is the maximum height h reached by the ball? consider air friction to be negligible. 1. h ≈ 10 m 2. h ≈ 50 m 3. h ≈ 30 m 4. h ≈ 40 m 5. h ≈ 20 m 003 10.0 points which of the two object shown below has the greatest kinetic energy? a m b 1 2 m v 2v 1. kinetic energies are the same. 2. a 3. b 4. unable to determine. 004 10.0 points tim, with mass 74.6 kg, climbs a gymnasium rope a distance of 3.1 m. the acceleration of gravity is 9.8 m/s 2 . how much potential energy does tim gain? answer in units of j. 005 10.0 points a car is moving at 64 miles per hour. the kinetic energy of that car is 5 × 105 j. how much energy does the same car have when it moves at 111 miles per hour? answer in units of j. 006 10.0 points an 102 kg man climbs up a 1 m high flight of stairs. the acceleration of gravity is 9.81 m/s 2 . w

Which statement correctly describes the current in a circuit that is made up of any two resistors connected in parallel with a battery? a. the current in the battery and in each resistor is the same b. the current the battery equals to the sum of the currents in the resistors c.the current in the battery is less than the current in either resistor d. the current in the battery equals to the product of the currents in the resistors

Ascientist notices that an oil slick floating on water when viewed from above has many different colors reflecting off the surface, making it look rainbow-like (an effect known as iridescence). she aims a spectrometer at a particular spot and measures the wavelength to be 750 nm (in air). the index of refraction of water is 1.3