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# olympiads.hbcse.tifr.res.in Indian National Physics Olympiad – INPhO 2016 : Homi Bhabha Centre For Science Education

** Name of the Centre **: Homi Bhabha Centre For Science Education

**: Indian National Physics Olympiad – INPhO 2016**

__Name Of The Exam__**: Physics**

__Name Of The Subject__**: Sample questions Papers**

__Document type__**: 2017**

__Year__** Website **: http://olympiads.hbcse.tifr.res.in/how-to-prepare/past-papers/

**Download Sample Question Paper :**

**: https://www.pdfquestion.in/uploads/13144-inpho2016.pdf**

__INPhO 2016__**: https://www.pdfquestion.in/uploads/13144-inpho2015.pdf**

__INPhO 2015__**: https://www.pdfquestion.in/uploads/13144-inpho2014.pdf**

__INPhO 2014__**: https://www.pdfquestion.in/uploads/13144-inpho2013.pdf**

__INPhO 2013__**: https://www.pdfquestion.in/uploads/13144-inpho2012.pdf**

__INPhO 2012__## Indian National Physics Olympiad :

** Time **: 09:00-12:00 (3 hours)

**: 50**

__Maximum Marks__

Related: Homi Bhabha Centre For Science Education Indian National Junior Science Olympiad 2016 : www.pdfquestion.in/13139.html

** Instructions **:

1. Write the last four digits of your roll number on every page of this booklet.

2. Fill out the attached performance card. Do not detach it from this booklet.

3. Booklet consists of 13 pages (excluding this sheet) and 6 questions.

4. Questions consist of sub-questions. Write your detailed answer in the blank space provided below the sub-question and all answer to the sub-question in the smaller box which follows the blank space. Note that your detailed answer will be considered in the evaluation.

5. Extra sheets are attached at the end in case you need more space. You may also use these extra sheets for detailed answer as well as for rough work. Strike out your rough work.

6. Non-programmable scientific calculator is allowed.

7. A mobile phone cannot be used as a calculator.

8. Mobiles, pagers, smart watches, slide rules, log tables etc. are not allowed.

9. This entire booklet must be returned.

**Please note that alternate/equivalent methods and different way of**

** expressing all solutions may exist.**

1.(a) A glass rod of refractive index 1.50 of rectangular cross section fd lg is bent into a \U” shape (see Fig. (A). The cross sectional view of this rod is shown in Fig.(B). Bent portion of the rod is semi-circular with inner and outer radii R and R + d respectively. Parallel monochromatic beam of light is incident normally on face ABCD.

(a) Consider two monochromatic rays r1 and r2 in Fig. (B). State whether the following statements are True or False.

(b) Consider the ray r1 whose point of incidence is very close to the edge BC. Assume it undergoes total internal reflection at p1. In cross sectional view below, draw the trajectory of this reflected ray beyond the next glass-air boundary that it encounters.

(c) Obtain the minimum value of the ratio R=d for which any light ray entering the glass normally through the face ABCD undergoes at least one total internal reflection.

(d) A glass rod with the above computed minimum ratio of R=d, is fully immersed in water of refractive index 1.33. What fraction of light flux entering the glass through the plane surface ABCD undergoes at least one total internal reflection?

2. A uniformly charged thin spherical shell of total charge Q and radius R is centred at the origin. There is a tiny circular hole in the shell of radius r (r R) at z = R. Find the electric field just outside and inside the hole, i.e., at z = R+ and z = R?? r).

3. This problem is designed to illustrate the advantage that can be obtained by the use of multiple-staged instead of single-staged rockets as launching vehicles. Suppose that the payload (e.g., a space capsule) has mass m and is mounted on a two-stage rocket (see figure). The total mass (both rockets fully fulfilled, plus the payload) is Nm.

(a) Obtain the velocity v of the rocket gained from the first-stage burn, starting from rest in terms of fV;N; n; rg.

(b) Obtain a corresponding expression for the additional velocity u gained from the second stage burn.

(c) Adding v and u, you have the payload velocity w in terms of N, n, and r. Taking N and r as constants, and the value of n for which w is a maximum. For this maximum condition obtain u=v.

(d) Find an expression for the payload velocity was of a single-stage rocket with the same values of N, r, and V .