Thursday, August 19, 2021

GRE Physics Problems - A Great Way To Test Blog Readers On Past Physics Posts

Dozens of intermediate to advanced posts on physics have appeared over the years since I began this blog.  They range from basic atomic physics, e.g.

To theoretical mechanics, e.g.

To Electromagnetic theory,  e.g.

To quantum mechanics:
A good way to test comprehension of those past topics is by trying your hand at GRE physics problems.  In that vein I will post a sequence of such problems from past GRE physics papers.  Solutions to the problems will typically follow in 1-2 days then another set will appear.   Here goes, for the first set  (You should allow for no more than 30 minutes, max):

1. The photo-electric threshold of tungsten is 2300A (where A denotes Angstrom). Estimate the energy E of the electrons ejected from the surface by ultraviolet light of wavelength 1800A.

2. Find the minimum energy in electron volts (eV) for an electron in a spark discharge to strip a sodium (Na) atom (Z = 11) of its last electron, assuming the other ten are already removed.

3. Let r^ be a position vector. Then find the divergence of r^.

4. Let r^ be a position vector and a be a constant vector. Then find the gradient of the scalar product: a*r^.

5. Consider the matrix:

(0........0........1)
(0........1.........0)
(1.........0 .......0)

a) Find Tr, the trace of the matrix

b) Find the eigenvalues of the matrix.

6. Let U1 and U2 be orthonormal functions. Find the value of N which normalizes:

F = N(U1 + 2i(U2)

7. Two men together support a uniform plank of wood. At the instant one of the men lets go of his end, what is the force the other man feels?

Questions 8-9:

Consider two coordinate systems whose origins are non-accelerating. Assume that one of these systems (denoted by primes) is rotating with constant angular velocity w with respect to the other which is non-rotating. (Let i' be one of three orthogonal unit vectors in the rotating system)

8. Find the time derivative in the non-rotating system.

9. Find the second order time derivative in the non-rotating system.

10. If two strings, whose densities are 25 g/cm and 9 g/cm are joined together then find the reflection coefficient for the vibration waves.

11. A particle of mass m moves in a plane  under the influence of a force F = - kr directed toward the origin. Show a polar coordinate system (r, theta) to describe the motion of the particle and thence or otherwise give the Lagrangian for the system.

12. According to relativistic mechanics the actual velocity of the electrons whose kinetic energy is 0.25Mev is what?

13. Compute the effective mass of a photon of wavelength 6000 A using the Einstein mass-energy equation.

Questions 14 and 15:

When the Sun is directly overhead, a given square meter surface of the Earth receives about 1300 watts of radiant energy. Assume this energy is in the form of a plane-polarized monochromatic wave.

14. Find the rms (root mean square) magnitude of the electric field of the wave.

15. Find the rms magnitude of the magnetic field for the wave.