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# Indian National Physics Olympiad –INPhO 2017 Question Paper : Homi Bhabha Centre For Science Education

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

**: Indian National Physics Olympiad –INPhO 2017**

__Name Of The Exam__**: Physics**

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

__Document type__**: 2017**

__Year__** Website **: https://olympiads.hbcse.tifr.res.in/

**: https://www.pdfquestion.in/uploads/13665-INPhO2017.pdf**

__Download Sample Question Paper__## Indian National Physics Olympiad –INPhO Question Paper :

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

**: 75**

__Maximum Marks__**:**

__Instructions__1. This booklet consists of 6 pages (excluding this sheet) and total of 6 questions.

2. This booklet is divided in two parts: Questions with Summary Answer Sheet and Detailed Answer Sheet. Write roll number at the top wherever asked.

Related: Homi Bhabha Centre For Science Education Indian National Junior Science Olympiad Question Paper : www.pdfquestion.in/13662.html

3. The final answer to each sub-question should be neatly written in the box provided below each sub-question in the Questions & Summary Answer Sheet.

4. You are also required to show your detailed work for each question in a reasonably neat and coherent way in the Detailed Answer Sheet. You must write the relevant Question Number on each of these pages.

5. Marks will be awarded on the basis of what you write on both the Summary Answer Sheet and the Detailed Answer Sheet. Simple short answers and plots may be directly entered in the Summary Answer Sheet. Marks may be deducted for absence of detailed work in questions involving loner calculations. Strike out any rough work that you do not want to be evaluated.

6. Adequate space has been provided in the answer sheet for you to write/calculate your answers. In case you need extra space to write, you may request for additional blank sheets from the invigilator. Write your roll number on the extra sheets and get them attached to your answer sheet and indicate number of extra sheets attached at the top of this page.

7. Non-programmable scientific calculators are allowed. Mobile phones cannot be used as calculators.

8. Use blue or black pen to write answers. Pencil may be used for diagrams/graphs/sketches.

9. This entire booklet must be returned at the end of the examination.

1. A massive star of mass M is in uniform circular orbit around a supermassive black hole of mass Mb. Initially, the radius and angular frequency of the orbit are R and ! respectively. According to Einstein’s theory of general relativity the space around the two objects is distorted and gravitational waves are radiated. Energy is lost through this radiation and as a result the orbit of the star shrinks gradually. One may assume, however, that the orbit remains circular throughout and Newtonian mechanics holds.

(a) The power radiated through gravitational wave by this star is given by where c is the speed of light, G is the universal gravitational constant, and K is a dimensionless constant. Obtain x and y by dimensional analysis.

(b) Obtain the total mechanical energy (E) of the star in terms of M, Mb [1] , and R.

(c) Derive an expression for the rate of decrease in the orbital period (dT/dt) in terms of the [3] masses, period T and constants.

2. The free surface of mercury (Hg) is a good reflecting surface. A tall cylinder partly filled with Hg and possessing total moment of inertia I is rotated about its axis with the constantangular velocity !0 as shown in figure. The Hg surface attains a paraboloidal profile. The radius of curvature of a general profile is given by where the symbols have their usual meaning.

(a) Obtain the expression for of the Hg surface in terms of !0, the distance x from the cylinder axis, and g. [3]

(b) Calculate the value of at the lowest point of the Hg surface, that is (0,0), when !0 = 78 rpm (revolutions per minute). [1]

(c) Consider a point object at (0,y0) as shown in the figure. Obtain an expression for the image position yi in terms of given quantities. State conditions on y0 for the formation of real and virtual images. [3]

3. Two identical blocks A and B each of mass M are placed on a long inclined plane (angle of inclination = ) with A higher up than B. The coefficients of friction between the plane and the blocks A and B are respectively µA and µB with tan > µB > µA. The two blocks are initially held fixed at a distance d apart. At t = 0 the two blocks are released from rest.

(a) At what time t1 will the two blocks collide?

(b) Consider each collision to be elastic. At what time t2 and t3 will the blocks collide a second and third time respectively? [4]

(c) Draw a schematic velocity-time diagram for the two blocks from t = 0 till t = t3. Draw below them on a single diagram and use solid line ( ) to depict block A and dashed line ( ) to depict block B. [5]