olympiads.hbcse.tifr.res.in INAO 2018 Sample Question Paper : Indian National Astronomy Olympiad
Name of the Centre : Homi Bhabha Centre For Science Education
Name Of The Exam : Indian National Astronomy Olympiad INAO – 2018
Name Of The Subject : Astronomy
Document type : Sample Questions/Past Papers
Year : 2018
Website : http://olympiads.hbcse.tifr.res.in/how-to-prepare/past-papers/
HBCSE INAO Sample Question Paper
Question Paper of Indian National Astronomy Olympiad INAO – 2018 Sample Question Paper and Answer key is now available in the official website of Homi Bhabha Centre For Science Education.
Related : Homi Bhabha Centre For Science Education INAO Indian National Astronomy Olympiad Questions Paper 2017 : www.pdfquestion.in/13647.html
General Instructions
** Please write your roll number on top of this page in the space provided.
** Before starting, please ensure that you have received a copy of the question paper containing total 4 pages (2 sheets).
** There are total 8 questions. Maximum marks are indicated in front of each sub-question.
** For all questions, the process involved in arriving at the solution is more important than the answer itself. Valid assumptions / approximations are perfectly acceptable. Please write your method clearly, explicitly stating all reasoning.
** Use of non-programmable scientific calculators is allowed.
** The answer-sheet must be returned to the invigilator. You can take this question booklet back with you.
Download Question Paper :
INAO 2018 : https://www.pdfquestion.in/uploads/INAO2018.pdf
Solutions : https://www.pdfquestion.in/uploads/INAO2018Sol.pdf
Model Questions
Duration: Three Hours
Maximum Marks: 100
1. In Newtonian mechanics force between two objects is felt instantaneously irrespective of distance. However, according to relativity, no interaction is truly instantaneous. For an object to feel the force, the information of the force is carried by eld particles. But nothing can travel faster than the speed of light.
Two friends, `A’ (a follower of Newton) and `B’ (a follower of Einstein), were once debating about what will happen to the Earth if the Sun suddenly vanishes. They both calculated the direction in which the Earth will go, when this calamity happens. What will be the angular dierence in the directions predicted by them? (5 marks)
2. Most buses in India run on diesel, whose caloric value is 44:8 106 J kg??1 and density is 0:832 kg l??1. A typical bus can go 3 km, on average, for every litre of diesel consumed. (a) (5 marks) Estimate power consumption of a typical bus.
(b) Calculate the maximum amount of solar power incident on roof of a typical bus. (3 marks)
(c) Best commercial solar cells in the market have an eciency of 20%. If the bus is to be run purely on solar power (during the day), estimate the area of solar cells required. What is the ratio of this area to the area of the rooftop of the bus. (2 marks)
3. The star Kepler-13A has a Jupiter-like planet (Kepler-13Ab) revolving around it. The period of revolution and rotation for this planet are equal. Analysis of the planet’s atmosphere has revealed that it contains vapourized Titanium Oxide (TiO), a key component in sunscreen lotions. Based on the boiling point of TiO, astronomers have estimated the temperature of Kepler-13Ab’s upper atmosphere to be about 3000 K.
(a) (7 marks) What is the orbital distance of Kepler-13Ab?
Given: Surface temperature of the star Kepler-13A = 7560 K, Radius of the star Kepler- 13A = 1.71 R
(b) (2 marks) Further analysis reveals condensed TiO as part of the lower atmosphere in Kepler-13Ab. Can you think of an explanation for this phenomenon?
4. Aditya is fascinated by the famous `innity corridor’ of IITB. The corridor is a very long, straight, roofed pathway connecting dierent departments. The roof of the corridor is sup- ported by square pillars of width b on either side. Let D be the distance between consecutive pillars on the same side and L be the width of the pathway (see gure).
(a) (8 marks) One day Aditya was standing at point M (see gure), in the middle of the corridor, looking ahead along the path. He found that he cannot see any object outside the corridor beyond the nth pillar on his either side. Derive an expression for n.
(b) (3 marks) Assume that the space between the successive pillars is D = 3 m, width of each pillar is b = 0:3m and width of the corridor is L = 5 m. Find numerical value of n.
(c) (4 marks) How will the answer in part (b) change, if Aditya was at position N instead of M (see gure) and looking through pillars along the top row of the gure?
5. Astronauts have found that the angular diameter of the Earth as seen from the surface of the Moon is 1:9. We assume that:
** the observer is standing on the equator of the Earth.
** the Moon is in the equatorial plane.
** the Moon’s orbit is circular.
(a) (10 marks) Find the time it takes for the Moon to completely rise above the Earth’s horizon.
(b) (3 marks) Brie y state why the three assumptions above are relevant to the solution.
(c) (2 marks) How much time would it take for the Earth to completely rise above Moon’s horizon?
6. (a) (3 marks) Let us say we are observing sky from a dark location and all planets are visible in the sky. Arrange the planets of the solar system in the descending order of their apparent brightness as observed from the Earth.
(b) (14 marks) Shinjini was observing the sky from a location on the equator on the night of 20-21 March and she made following observations in her diary.
** Today is 11 days prior to the full Moon.
** Saturn is seen in constellation of Sagittarius.
** Jupiter is seen rising at the time of the Moon set.
** Mars’ position was coinciding with the centre of Milky Way.
** Mercury set about 2 hours before the Moon.
** Venus was seen in the evening sky for about 2 hours after sunset.
In the answersheet, you will nd a circle which is passing through East, Zenith (point exactly above the head of the observer), West and Nadir (point exactly below the ob- server). Use the information given above to mark positions of the Sun, the Moon and the 5 planets on this circle at 11 am on the Vernal Equinox day (21st March). For each object, write a 1-2 line explanation stating why you think it is the correct position of the object.
7. Yash discovered a binary star, consisting of a very light star A in a circular orbit around a massive star B (mA mB). He could measure the component of velocity of star A along the line of sight via Doppler shift. His measurements are tabulated below. All the data were obtained on 17th July 2009, and the times given are in UT.
(a) (10 marks) Plot the data, and measure the orbital period of star A from the plot.
(b) (5 marks) Use this information to calculate the mass of star B, in terms of solar mass.
(c) (3 marks) Is the plot symmetric with resepect to time axis? If yes, what does it signify? If no, what is the reason?
8. In this question, we will investigate construction of large mirrors of modern telescopes.
(a) (2 marks) Typical large modern telescopes do not have a single (monolithic) mirror. Instead, the mirror is divided in many small hexagonal concave mirror segments. Suppose one such telescope has segments with individual focal length of 30m and length of their hexagonal side is 87:5 cm. What is the distance between two parallel edges of such a mirror segment?
(b) (6 marks) To avoid image distortion (due to spherical aberration), the telescope mirrors are made in the shape of paraboloid of revolution (a parabola rotated around its axis). Let us take one such mirror facing upwards and observing a star at zenith (exactly overhead). As you may be aware, such a parabola follows equation of x2 = 4ay, where a is the distance of the focus of the parabola from its vertex. You may also recall that slope of a tangent to the parabola at any point (x0; y0) is given by x0=2a. Show that all rays from the star will converge at the focus of the parabola.
(c) (3 marks) In part (b) above, show that all these rays will arrive at the focus in same phase.
Solutions
1. According to A, the force eect is instantaneous.
So, as soon as Sun disappears, Earth ies o tangentially. 1 M
According to B, the eect of disappearance of the Sun is felt with delay of 499 s. 1 M
In this time, the Earth would have moved by angle of
499/ 360
86400/ 365:25
= 0:0056 = 20:4900 = 9:77 10??5 rad
Thus, the angular dierence in the direction calculated by both of them will be 20:4900
2. Typical speed of bus in city = 18kmh??1 to 36kmh??1
Typical speed of bus on highway = 36kmh??1 to 72kmh??1
Considering eciency of bus 3kml??1 and speed 30kmh??1 2 M) Time to burn 1 litre of diesel is t = 3 30
3600 = 360 s 1 M Power consumed by bus is, P= 44:80 106 0:832 360 103:5kW 2 M
Accepted range for power consumption of bus is 75 kW to 300 kW, i.e. 100 hp to 200 hp
Typical rooftop area of bus in India 10m 2:5m = 25m2 (accepted range 10m2 to 30m2)
Total solar energy received by bus = 1:366 10 2:5 34:15kW
This assumes that all energy is incident perpendicularly on the rooftop, i.e. the Sun is directly overhead 1 M Considering eciency of typical commercially available solar cell is 20%,
Total solar energy available for consumption is 0:2 34:15kW = 6:83 kW. 1 M
For minimum power consumption area of rooftop should be 103:5 6:83 15 times more than that of present.
3. Realize that the planet is tidally locked, which means only one hemisphere of the planet will receive radiation from the star at all times, and we have to consider the contribution to blackbody output of the planet only from this hemisphere.
Let that surface temperature of Kepler-13A, Ts = 7560K
Let radius of Kepler-13A, Rs = 1:71R Using Stefan-Boltzmann’s Law,
Ls = 4R2 sT4