Question 1

The Event Horizon Telescope Collaboration took the first photo of the shadow of a supermassive black hole in the galaxy M87 (see photo below) in 2019. What is the source of the bright light surrounding the black hole?

(a) Hawking radiation
(b) Star light from behind the black hole
(c) Hot plasma spiraling into the black hole
(d) None of the above

Question 2

Which of the following statements about black holes are correct?

(a) I and II
(b) II only
(c) III only
(d) II and III

Question 3

The photo below was taken during the Venus Transit in 2004. It is known that the size of Venus’ orbit around the Sun is about 0.7 that of the Earth’s, both approximately circular. What is Venus’ radius in Solar radius?

(a) 1%
(b) 0.1%
(c) 0.01%
(d) 10%

Question 4

When we look up the sky at a clear dark night, we can see many stars (see photo below). If we gaze at the same stars 1 million years from now, which of the following statements are correct?

(a) I and II
(b) II only
(c) III only
(d) II and III

Question 5

Dirty clothes containing grease and oil stains are cleaned by adding detergents to water, stains are removed because detergent:

(a) Reduces the surface tension between water and oil drastically
(b) Increases the surface tension between water and oil
(c) Increases the viscosity of water and oil
(d) Decreases the viscosity in detergent mixed water

Question 6

If the door of a running refrigerator in a closed room is kept open, what will be the net effect on the room?

(a) It will cool the room
(b) It will heat up the room
(c) It will make no difference on the average
(d) It will make the temperature go up and down

Answer

Question 1: (c) Hot plasma spiraling into the black hole
Gas being trapped and accreted into a black hole would become very hot, so that the gas become ionised, forming a hot plasma. The plasma is so hot that it glows. Hawking radiation is too weak to be seen. It is indeed true that the strong gravity of the black hole would bend light and therefore direct some of the star light from behind the black hole to us. However, those are also too weak compared with the light emitted by the plasma.

Question 2: (b) II only
I is wrong. The radius of the event horizon of a non-rotating black hole is proportional to its mass M, and so its volume is proportional to M³. The density of a non-rotating black hole is therefore inversely proportional to its mass squared (M^-2). A supermassive black hole such as the one at the center of M87 imaged by Event Horizon Telescope (M = 6.5 billion solar mass) has a density 2x10^-20 times that of a solar mass black hole, or 3x10^-4 that of the Sun.

II is correct. Any deviation from spherical shape of the event horizon of a non-rotating black hole would be quickly dissipated by emitting gravitational waves.

III is wrong. Stars with mass less than 2-3 solar masses would collapse to a high density and the electron or neutron degeneracy pressure of its materials would be able to support the star, forming white dwarfs or neutron stars, instead of black holes.

Question 3: (a) 1%
In the photo, the radius of Venus is about 3% that of the Sun. So Dθ = r = 0.03R_s, where D is the Earth-Sun distance (1 AU), θ is the angular size of Venus as observed on the Earth, r is the radius of Venus’ shadow on the Sun, and R_s is the radius of the Sun. The radius of Venus is rV = 0.3Dθ. Therefore, rV = 0.3Dθ = 0.03r = 0.009 R_s.

Question 4: (d) II and III
I is wrong. All stars we can see with naked eye are within our galaxy, the Milky Way. Stars in a galaxy are bounded together by their mutual gravity, and so a galaxy would not expand with the expansion of the universe. Most stars would look more or less the same over 1 million years, which is much shorter than the typical lifetime of a star.

II is correct. Most of the bright stars making up the constellation patterns are nearby stars (hundreds of light years in distance). Over a million year, our relative positions with these nearby stars would have changed significantly.

III is correct. On average, there would be about 1 supernova (a star that explodes when it dies) in each galaxy per 100 years. After a supernova explosion, the remnant can form either a neutron star or a black hole, neither of which can be seen with naked eye from afar.

Question 5: (a) Reduces the surface tension between water and oil drastically
Surface tension is the property of the surface of a liquid that allows it to resist an external force, due to the cohesive nature of its molecules. When surface tension is reduced, water wets things more uniformly, spread over surfaces and seep into dirty clothes fibres. Once the grease is broken up into smaller pieces, it can be carried away by water easily.

Question 6: (b) It will heat up the room
It will heat up the room because heat from the inside of the refrigerator is released into the room, counter acting any cooling effect, plus the energy that is used to operate the compressor eventually winds up being heated, therefore increasing the room temperature.