Nuclear & Particle Physics - Beta Decay

When the beta decay of ⁶⁰Co nuclei is observed at low temperature in a magnetic field that aligns spins of the nuclei, it is found that the electrons are emitted preferentially in a direction opposite to the ⁶⁰Co spin direction. Which of the following invariances is violated by this decay

A. Gauge invariance
B. Time invariance
C. Translation invariance
D. Reflection invariance
E. Rotation invariance

(GR9677 #34)

Solution:

Wu experiment, 1957: beta decay of Cobalt-60 shows that electrons are emitted preferentially in a direction opposite to the ⁶⁰Co spin direction → Parity violation by the weak interaction.

A. Gauge invariance → related to conservation of charge
B. Time invariance → energy
C. Translation invariance → momentum
D. Reflection invariance → parity
E. Rotation invariance → angular momentum

Answer: D

Electromagnetism - Conductor

A conducting cavity is driven as an electromagnetic resonator. If perfect conductivity is assumed, the transverse and normal field components must obey which of the following conditions at the inner cavity walls?

A. E_n = 0, B_n = 0
B. E_n = 0, B_t = 0
C. E_t = 0, B_t = 0
D. E_t = 0, B_n = 0
E. None of the above

(GR9277 #34)

Solution:

Boundary Condition on the surface of perfect conductor:

• E_tangential = 0
• E_normal ≠ 0 → (A) and (B) FALSE
• B_tangential ≠ 0 → (C) FALSE
• B_normal = 0

Answer: D

Classical Mechanics - Conservative Force

Question 34-36

The potential energy of a body constrained to move on a straight line is kx⁴ where k is a constant. The position of the body is x, its speed v, its linear momentum p, and its mass m.

The force on the body is

A. ½mv²
B. −4kx³
C. kx⁴
D. −kx⁵/5
E. mg

(GR8677 #34)

Solution:



Answer: B

Special Relativity - Space-Time Interval

In an inertial reference frame S, two events occur on the x-axis separated in time by Δt and in space by Δx. In another inertial reference frame S’, moving in the x-direction relative to S, the two events could occur at the same time under which, if any, of the following conditions?

A. For any values of Δx and Δt.
B. Only if 
C. Only if 

D. Only if 
E. Under no condition

(GR0177 #34)

Solution:

The Invariant Space-Time Interval:  ΔS² = Δx² − (cΔt)² 

For the two events occur at the same time: ΔS²  0
Δx² − (cΔt)²  0
Δx²  (cΔt)²
(Δx/Δt)²  c²
|Δx/Δt|  c

Answer: C