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A block of mass 5 kg is placed on a frictionless inclined plane making an angle of 3 0 with the horizontal. Calculate the acceleration
A block of mass kg is placed on a frictionless inclined plane making an angle of with the horizontal. Calculate the acceleration of the block and the time it takes to slide meters down the plane from rest.
Electromagnetism:
A circular loop of radius meters carries a current of A Calculate the magnetic field at the center of the loop.
Thermodynamics:
A Carnot engine operates between two heat reservoirs at temperatures of K and K If the engine absorbs J of heat from the hot reservoir, calculate the work done by the engine and the heat rejected to the cold reservoir.
Optics:
A doubleslit experiment is performed with light of wavelength nm The slits are separated by mm and the screen is meters away from the slits. Calculate the distance between the central maximum and the firstorder maximum on the screen.
Quantum Mechanics:
Calculate the energy of the first excited state of an electron in a onedimensional infinite potential well of width nm Use the particle in a box model.
Electric Circuits:
A series RLC circuit has a resistance of ohms, an inductance of H and a capacitance of
F Calculate the resonant frequency of the circuit.
Relativity:
Calculate the relativistic kinetic energy of an electron moving at c where
c is the speed of light.
Fluid Mechanics:
Water flows through a pipe of diameter meters with a velocity of ms Calculate the Reynolds number and determine whether the flow is laminar or turbulent. Assume the kinematic viscosity of water is
m
s
Astrophysics:
Calculate the Schwarzschild radius of a black hole with a mass times that of the Sun. Use the formula
R
s
c
GM
where
G is the gravitational constant,
M is the mass, and
c is the speed of light.
Nuclear Physics:
A sample contains gram of
U Calculate the number of
U atoms in the sample and the activity decay rate if the halflife of
U is
years.
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