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Here we give a simple example of how one can estimate the limit of x to infinity of a function f(x) given by its Taylor expansion around x = 0
Consider a Mach-Zehnder interferometer where in one arm we place a filter with a transmission coefficient f << 1.
A person moves 30m north, then 20m east and then 30 H (square root 2) m 45 degrees south of west. His displacement from the original position is.
Two planes leave simultaneously from the same airport, one flying due north and the other flying due east.
Find the center of mass of a system of three particles of mass 2 kg, 3kg and 4 kg placed at the corners of an equilateral triangle of side 2 meters.
Find the coordinates (xcm, ycm) of the c.m. of the system.Three point masses are located in an x,y plane as follows.
A wire of density 9gm/cm^3 is stretched between two clamps 100cm apart subjected to an extension of 0.05 cm.
The motion of two bodies interacting only with each other by central forces can be reduced to an equivalent one body problem.
Find the characteristic frequencies and the characteristic modes of vibration for the 2 situations.
Calculate the change in temperature of 10^(-3) m^3 of lead undergoing a reversible and adiabatic compression from 1 to 1000 atms.
Find the entropy change of an ideal gas and of a van der Waals gas in case of isothermal expansion in which the volume increases by a factor alpha.
A point charge +q is situated a distance a (a>R)from the center of a grounded conducting sphere of radius R. Find the potential outside the sphere.
Derive Maxwell's Relations from First and Second Laws of Thermodynamics and Thermodynamic Functions like Internal Energy.
Consider a flexible string held stationary at both ends and free to vibrate transversely subject only to the restoring forces due to tension in the string.
How long would it take sunlight to melt 2 meters (thick) of snow on a mountainside ? Assume that the snow is 50% snow and 50% air.
Find the average number of open links and show that for low temperature kT is independent of N.
Count the number of microstates that correspond to the macrostate in which the total energy of the system is E =ne where is an integer.
The acceleration of a marble in a certain fluid is proportional to the speed of the marble squared and is given in SI units) by a=-3.00 v^2 .
How long will it take to fill the pool to a depth of 1.2m if water issues from the hose at a speed of 0.33m/s?
What gauge pressure in the water mains is necessary if a firehose is to spray water to a height of 15m?
Calculate the power output of the heart, in watts, assuming 70 beats per minute.
A U-shaped tube, open to the air on both ends, contains mercury. Water is poured into the left arm until the water column is 13.1 cm deep.
A U tube open at both ends is partially filled with water. Oil having a density of 750 kg/cubic meter is then poured into the right arm.
Water is pumped through a pipe to a tank at the top of a building. The pressure of the water at ground level is 2.2* 10^5 Pa and at the tank.
A log of wood is floating in water with 40% of its volume above the surface of the water. if the volume of the log is 0.4 m^3, find the mass of the log.