Download Sample Math problems

Sample Math problems
These problems are meant to be representative of what you need to know for the final.
They are not exactly the problems that will appear in the final exam, but they do require
the same set of skills. They might not cover all the formulas and equations that we have
seen in the class. I recommend going back and rework the problems in the homework to
study for the final and to have a look at the in-class quizzes.
1) From laboratory measurements, we know that a particular spectral line formed by
hydrogen appears at a wavelength of 486.1 nanometers (nm). The spectrum of a
particular star shows the same hydrogen line appearing at a wavelength of 485.9 nm.
What can we conclude?
a) The star is getting colder
b) The star is moving away from us
c) The star is expanding
d) The star is moving toward us
e) The star is getting hotter.
2) From laboratory measurements, we know that a particular spectral line formed by
sodium appears at a wavelength of 589.6 nanometers (nm). You measure the same line
in a distant star to be at a wavelength of 589.4 nm. What is the velocity of the star?
a) 6000 km/s toward Earth
b) 101.7 km/s toward Earth
c) 6000 km/s away from Earth
d) 101.7 km/s away from Earth
e) We cannot calculate its velocity if we do not know the temperature first.
3) The nearest star to the Sun, Proxima Centauri, has a luminosity of 1.7 x 1023 Joules/
second. It has an age of 5 billion years and a mass of 2x1029 kg. How much mass has it
lost through hydrogen fusion reactions over its lifetime so far? You can assume its
luminosity has been constant.
a) 2.2 x 1016 kg
b) 1.9 x 106 kg
c) 2.9 x 1023 kg
d) 3.5 x 1029 kg
e) 2.2 x 101 kg
4) What is the Scwarzschild radius of a 100 million-solar-mass black hole?
a) 3 million km
b) 3 km
c) 30 km
d) 300 million km
e) 3,000 km
5) [FIXED] When my cat and I are in the same reference frame, I measure its tail to be 13
inches long. The other day my cat saw another cat outside of the window and flew past
me at 0.75c. How long did I measure its tail to be as it flew by?
a) 8.6 inches
b) 6.5 inches
c) 0.43 inches
d) 3.25 inches
e) 7.31 inches
6) Recall that Hubble's law is written v = H0d, where v is the recession velocity of a
galaxy located a distance d away from us, and H0 is Hubble's constant. Suppose H0 = 65
km/s/Mpc. How fast would a galaxy located 500 megaparsecs (Mpc) distant be
receding from us?
a) 32500 km/s
b) 65 km/s
c) 0.65 times the speed of light
d) 65 Mpc/s
e) 9 km/s
7) We have this particular iron line that we need to measure in the spectra of a galaxy.
This line, in the laboratory has been found at 5110Å. All we know is that this galaxy has
a cosmological redshift of 0.2. At what wavelength would we find this line in the
spectrum?
a) 5110 Å
b) 1022 Å
c) 4088 Å
d) 6132 Å
e) 2555 Å
8) One student, obsessed with his low weight, overheard you studying for the final. He
decided that in order to qualify for a wrestling TV show, he would try to measure his
weight while moving really fast. He needs to weight at least 300 kg to get into the TV
show but the last time he measured his weight (at rest) he was only 130 kg. He comes to
you and asks you: How fast should I go to get into the TV show?
You know this would not work, but you take the opportunity to help out and study at
the same time. What would you answer?
a) 0.9 c
b) 0.75 c
c) 0.6 c
d) 20 miles/hr
e) 30,000 miles/hr
9) How does the force of gravity on the surface of a 1 solar mass neutron star compares
to the gravity on the surface of the sun? The radius if the Sun is 6.9 x 105 km, and you
can assume that the radius of the neutron star is about 7km.
a) The force on the Sun is about 105 times stronger than on the neutron star
b) The force on the Sun is about 102 times weaker than on the neutron star
c) The force on the Sun is about 105 times weaker than on the neutron star
d) The force on the Sun is about 1010 times weaker than on the neutron star
e) The force on the Sun is about 1010 times stronger than on the neutron star
Correct answers:
1)D
2)B
3)C
4)D
5)A
6)A
7)D
8)A
9)D