Name of the Organization : Homi Bhabha Centre For Science Education
Name Of The Exam : Indian National Physics Olympiad - 2017
Document Type : Sample Question Paper
Subject : Physics
Year : 2017

Website : http://olympiads.hbcse.tifr.res.in/?page_id=1376#QS
Download Model/Sample Question Papers : http://www.indianjobtalks.com/upload...-INPhysics.pdf

Indian National Physics Olympiad Question Paper :
Time : 09:00-12:00 (3 hours)
Maximum Marks: 75

Instruction :
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.
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.

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 LG = KcxGyM2R4!6
(b) Obtain the total mechanical energy (E) of the star in terms of M, Mb and R.
(c) Derive an expression for the rate of decrease in the orbital period (dT/dt) in terms of the 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 constant angular 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 [3] axis, and g.
(b) Calculate the value of at the lowest point of the Hg surface, that is (0,0), when !0 = 78 rpm [1] (revolutions per minute).
(c) Consider a point object at (0,y0) as shown in the figure. Obtain an expression for the image [3] position yi in terms of given quantities. State conditions on y0 for the formation of real and virtual images.

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

4. One mole of an ideal gas (cp/cv = where symbols have their usual meanings) is subjected to an Otto cycle (A-B-C-D) as shown in the following PV diagram. Path A-B and C-D are adiabats. The temperature at B is TB = T0. Diagram is not to scale.
(a) Find the temperatures at A,C, and D in terms of T0 and pressures at A and D in terms of [4] P0.
(b) Find total heat absorbed (Q) by the system, the total work done (W) and efficiency () [31/2] of the Otto cycle in terms of and related quantities.
(c) Draw below corresponding P-T and T-S(entropy) diagrams for the cycle.