Question 1

Which of the following best describes the 'Wave in Ether' model of light as proposed in the 19th century?

Accepted Answer

Light propagates as a disturbance in a hypothetical medium called ether, similar to how sound travels through air.

Question 2

Assuming the 'Particle in Vacuum' model, which statement about the speed of light is most reasonable?

Accepted Answer

The speed of light depends on the motion of the source emitting the light.

Question 3

In the 'Wave in Ether' model, if you move toward a light source with speed $$v$$ while at rest in the ether, what speed do you observe for the wavefronts of light?

Accepted Answer

You observe the wavefronts passing at speed $$c + v.$$

Question 4

What was the main result of Thomas Young's 1802 experiment, and what did it imply about the nature of light?

Accepted Answer

It demonstrated interference patterns, supporting the wave model of light but not definitively disproving the particle model.

Question 5

According to Einstein's 1905 speed of light principle, which statement is correct?

Accepted Answer

The speed of light $$c is $$constant in all inertial frames, regardless of the motion of the source or observer.

Question 6

Which two physicists in the 1800s were most influential in developing the Ether model of light?

Accepted Answer

James Clerk Maxwell and Hendrik Lorentz

Question 7

Which experiment was designed to detect the motion of the Earth relative to the ether and resulted in a 'null' result?

Accepted Answer

Michelson–Morley experiment

Question 8

Why does the interpretation that 'the Earth drags the ether' conflict with the observed phenomenon of stellar aberration?

Accepted Answer

Stellar aberration requires that the ether is stationary and not dragged by the Earth, otherwise the observed shift in star positions would not occur.

Question 9

In Newtonian gravity, what is the relationship between the orbital radius $$r_0$$ and orbital speed $$v_0$$ for a planetesimal orbiting the Sun?

Accepted Answer

$$v_0$$ = \sqrt{\frac{GM}{$$r_0$$}}$$

Question 10

After Neptune reduces Halley's speed from $$v_0 to$$ $$\alpha v_0$ ($$\alpha \u003c 1$$), what happens to Halley's orbit?

Accepted Answer

Halley's orbit becomes elliptical with the Sun at one focus, and the aphelion distance equals the original orbital radius $$r_0.$$

Question 11

Using conservation of angular momentum, what is the relationship between the perihelion distance $$r_p$$ and the aphelion distance $$r_a$$ for Halley's new orbit?

Accepted Answer

$$r_p = \frac{\alpha}{\beta} r_0$

Question 12

Using conservation of energy, what is the expression for $$\beta ($$the ratio of perihelion speed to original speed) in terms of $$\alpha$$?

Accepted Answer

$$\beta = \frac{2 - \$$alpha^2$$}{\alpha}$$

Question 13

If $$\alpha \rightarrow 0 ($$Halley's speed is reduced to nearly zero), what happens to the perihelion distance $$r_p$$?

Accepted Answer

$$r_p \rightarrow 0$$; Halley falls almost directly toward the Sun.

Question 14

If Neptune increases Halley's speed to $$v_a = \sqrt{2} v_0$, what happens to Halley's orbit?

Accepted Answer

Halley reaches escape velocity and its orbit becomes parabolic.

Question 15

What is the formula for the semimajor axis $$a of $$Halley's new elliptical orbit in terms of $$r_a$$ and $$r_p$$?

Accepted Answer

$$a = \frac{r_a + r_p}{2}$$

Question 16

Given $$r_a = (1 + e)a$$ and $$r_p = (1 - e)a$$, what is the eccentricity $$e in $$terms of $$\alpha$$?

Accepted Answer

$$e = |1 - \$$alpha^2$$|$$

Question 17

Which of the following best illustrates the difference between Lorentz-FitzGerald contraction and Einstein's length contraction?

Accepted Answer

Lorentz-FitzGerald contraction is a physical contraction of matter relative to the ether, while Einstein's length contraction arises from the geometry of spacetime.

Question 18

According to Einstein's universal relativity principle, which statement is true?

Accepted Answer

No physical experiment performed in a closed room moving with constant velocity can detect the motion of the room.

Question 19

Which concept is ruled out by Einstein's universal relativity principle?

Accepted Answer

The existence of absolute velocity

Guided Study: Newtonian Gravity and Special Relativity Concepts

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