physics_auth wrote:SAMPLE QUESTION 24
A neutral particle is at rest in a uniform magnetic field of magnitude B. At time t = 0 it decays into two charged particles each of mass m. The two particles move off in separate orbits, both of which lie in a plane perpendicular to the magnetic field. The charge of one of the particles is +q. What is going to happen at a future time t > 0?
(A) The particles will collide after a time interval equal to 2πm/qB.
(B) The particles will collide after a time interval equal to πm/qB.
(C) The particles will collide after a time interval equal to πm/2qB.
(D) The particles will recede from each other until they are infinitely apart.
(E) The particles will recede from each other, moving along a straight line and subsequently approach each other (moving along the same line) under the action of the mutual Coulomb attraction.SAMPLE QUESTION 25
A point charge +Q is placed at the vertex of a cube. What is the electric flux through the cube?
(E) +SAMPLE QUESTION 26
The mass density of a certain planet has spherical symmetry but varies in such a way that the mass inside every spherical surface with center at the center of the planet is proportional to the radius of the surface. If r is the distance from the center of the planet to a point mass inside the planet, the gravitational force on this mass is:
(A) not dependent on r
(B) proportional to
(C) proportional to r
(D) proportional to
(E) proportional to SAMPLE QUESTION 27
: (This is a tough question - a more analytical answer is provided in the thread below)
A soap film immersed in air is illuminated by white light almost normal to its surface. The index of refraction of the film is 1.50. Wavelengths of 480 nm and 800 nm are ONLY intensified in the reflected beam. (No other wavelengths between them are intensified.) The thickness of the film is:
(A) 150 nm
(B) 240 nm
(C) 360 nm
(D) 400 nm
(E) 600 nmSAMPLE QUESTION 28
A certain nucleus, after absorbing a neutron, undergoes beta minus decay and then splits into two alpha particles. Which of the following can be the A and Z of the original nucleus?
(A) A = 6 _____ Z = 2
(B) A = 6 _____ Z = 3
(C) A = 7 _____ Z = 3
(D) A = 7 _____ Z = 2
(E) A = 8 _____ Z = 4SAMPLE QUESTION 29
The energy supplied by a thermal neutron in an induced fission event is essentially equal to:
(A) its rest energy
(B) its kinetic energy
(C) its binding energy to the nucleus which undergoes fission
(D) the total energy of the initial fission fragments
(E) the energy released during the fission processSAMPLE QUESTION 30
A baryon with strangeness 0 decays into two particles, one of which is a baryon with strangeness +1. Which of the following could be the other particle?
(A) a baryon with strangeness 0
(B) a baryon with strangeness -1
(C) a lepton
(D) a meson with strangeness +1
(E) a meson with strangeness -1SAMPLE QUESTION 31
Two bodies move with speeds 0.8c and 0.6c respectively. If the two bodies have the same rest mass, what is the ratio of their relativistic kinetic energies?
(E) 32/27SAMPLE QUESTION 32
A large transparent slab of uniform thickness and index of refraction
is initially immersed in the air. A monochromatic beam of light is incident on the slab at an angle
such that the reflected and the refracted beam emerge on mutually orthogonal directions. The previous experiment is then repeated (i.e. same angle of incidence for the aforementioned monochromatic beam), this time with the slab immersed in a liquid with index of refraction
. In terms of the angle of incidence
and the refraction indices
, what is the angle between the emergent reflected and refracted beams in the latter case?
(A) They are still orthogonal to each other.
(B) It is equal to
(C) It is equal to
(D) It is equal to
(E) It is equal to
.SAMPLE QUESTION 33
The largest number of beats per second will be heard from which of the following pairs of tuning forks?
(A) 200 and 201 Hz
(B) 256 and 260 Hz
(C) 534 and 540 Hz
(D) 763 and 774 Hz
(E) 8420 and 8422 HzSAMPLE QUESTION 34
A beam of particles of energy E = 9 eV strikes on a step potential and 25% of the beam's particles is reflected back. What is the height of the step potential?
(A) 4 eV
(B) 8 eV
(C) 3 eV
(D) 1 eV
(E) 5 eVSAMPLE QUESTION 35
The magnetic dipole moment of a current-carrying loop of wire is in the positive z direction. The magnetic dipole is placed in space where there is a magnetic field
is some positive constant and
the unit vectors along directions x and y respectively. What is the direction of the magnetic torque on the loop?
(A) It is along the negative z direction.
(B) It is along the line y = -x in the forth quadrant.
(C) It is along the line y = x, in the third quadrant.
(D) It is along the line y = -x, in the second quadrant.
(E) It is along the line x = y = z towards positive x,y and z.SAMPLE QUESTION 36
A system is composed of 4000 non-interacting particles distributed among three possible energy states
. A particular partition corresponds to the occupation numbers
for the first two energy states. The total number of particles of the system remains constant. What is approximately the average energy of this configuration?
(E) SAMPLE QUESTION 37
The positive terminals of two batteries with emf's of
, respectively, are connected together. It is
. The circuit is completed by connecting the negative terminals. If each battery has an internal resistance r, what is the rate with which electrical energy is converted to chemical energy in the smaller battery?
(E) SAMPLE QUESTION 38
The Lagrangian for a mechanical system is
is a generalized coordinate and
. What is the Hamiltonian
of this system?
(E) SAMPLE QUESTION 39
Massless and inextensible string is wrapped around the periphery of a homogeneous cylinder of radius R = 0.5 m and mass m = 2 kg. The string is pulled straight away from the upper part of the periphery of the cylinder, without relative slipping. The cylinder moves on a horizontal floor, for which the friction coefficient (μ) is 0.4. What is most nearly
the maximum force
that can be exerted on the free end of the string so that the cylinder rolls without sliding?
= 24 N
= 12 N
= 8 N
= 6 N
= 8/3 NSAMPLE QUESTION 40
Which of the following facts could be a remnant of the Big Bang theory for the evolution of the universe from a space-time singularity?
I. Uniform distribution of microwave background radiation.
II. Uniform distribution of background electrons.
III. Uniform distribution of background neutrinos.
IV. Uniform distribution of gluons and quarks.
(A) I and II only
(B) I, II and III only
(C) I and III only
(D) I, III and IV only
(E) II and III onlySAMPLE QUESTION 41
Six identical point charges +q are placed on the vertices of a regular hexagon of side of length l. There is one charge on each vertex. The hexagon is rotated about an axis that passes through its center of symmetry and is perpendicular to its plane. If the frequency of revolution is f, what is the magnitude of the induced magnetic field B at the center of the hexagon?
= magnetic susceptibility of free spaceSAMPLE QUESTION 42
A Carnot engine operates using a monoatomic gas as its working substance. Which of the following procedures could lead to the greatest possible increase of the efficiency of the Carnot thermal engine?
(A) The increase of the temperature of the hot reservoir by 40 K.
(B) The lowering of the temperature of the cold reservoir down to 0 K.
(C) The substitution of the monoatomic gas by a diatomic gas.
(D) The increase of the temperature of the hot reservoir by 20 K and the simultaneous decrease of the temperature of the cold reservoir by 20 K.
(E) The substitution of the reversible mode of operation of the engine by an irreversible one.