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# (Download) Indian National Astronomy Olympiad (INAO) Question Papers 2018

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## (Download) Indian National Astronomy Olympiad (INAO) Question Papers 2018

Question paper
Exam Name :
INAO Olympiad Question Papers 2018

1. (5 marks) 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 field 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 difference in the directions predicted by them?
2. Most buses in India run on diesel, whose calorific 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) (3 marks) Calculate the maximum amount of solar power incident on roof of a typical bus.
(c) (2 marks) Best commercial solar cells in the market have an efficiency 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.
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 Kepler13A = 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?