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|c denotes partial differentiation wrt coordinate xc and ||c denotes covariant differentiation wrt coordinate xc .
1. Consider an observer falling freely towards the centre of a Schwarzschild vacuum 15 region of spacetime, that is, falling radially inwards. Using the usual choice for the Schwarzschild coordinates, (t, r), derive the equations of motion of this observer, and in particular derive equations that give the proper time, τ , of the observer and the radial coordinate of the observe, r. Consider the three cases:
(a) The observer falls from from rest at a radial position r = r0.(b) The observer falls from rest at r = ∞.(c) The observer falls from infinity, where the radial velocity was v∞ relative to a locally static observer at r = ∞.In some cases, your solution can be given in parametric form.
A coil has 395 turns and self-inductance 3.25 mH. The current in the coil varies with time according to i = (680 mA) cos(?t/0.0250 s). What is the maximum emf induced in the coil
Express the power in terms of some or all of the variables given in the problem introduction.
A 64 kg skier coasts up a snow-covered hill that makes an angle of 25° with the horizontal, What is the magnitude of the kinetic frictional force
Heat is added to two identical samples of a monatomic ideal gas. In the first sample the heat is added while the volume of the gas is kept constant, By how much does the temperature of this sample increase
A medium sized home may have a roof with a surface area of 120m2. Find the total amount of solar energy incident on the roof in one day
The acoustical system is driven by speaker emitting a 432Hz note. If destructive interference occurs at a particular instant, by what least amount amount must the difference of two path lengths in the U-shaped tube be increased so as to hear const..
You have a thin metal sphere of unknown volume that contains helium gas at low pressure. Given that the volume of the metal sphere, pressure gauge, etc., was 341 mL, how many moles of helium gas would you have
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what are the magnitude and direction of its acceleration. find out the magnitude of the charge on the moving particle.
A 20.0%u03BCF capacitor is charged by a 160.0-VV power supply, then disconnected from the power, Calculate the oscillation frequency of the circuit
If 200 g of water is contained in a 300g aluminum calorimeter at 20°C and 20g of steam at 100°C is introduced into the calorimeter
An advertisement shows a 1239 kg car slowly pulling at constant speed a large passenger airplane to demonstrate the power of its newly-designed 89.7-hp (horsepower) engine, Calculate the force that opposes the motion
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