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# HBCSE INPho Sample Question Paper 2018 Indian National Physics Olympiad : Homi Bhabha Centre For Science Education

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

**: INPho Indian National Physics Olympiad – 2018**

__Name Of The Exam__**: Physics**

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

__Document type__**: 2018**

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

__Website__## HBCSE INPho Sample Questions Paper

Question Paper of INPho Indian National Physics Olympiad 2018 Sample Questions and model Solutions is now available in the official website of Homi Bhabha Centre For Science Education.

: Homi Bhabha Centre For Science Education HBCSE INJSO Questions Paper 2018 : www.pdfquestion.in/29895.htmlRelated

## Instructions

1. This booklet consists of 27 pages (excluding this sheet) and total of 7 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(s) 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.

6. Adequate space has been provided in the answersheet for you to write/calculate your answers. In case you need extra space to write, you may request additional blank sheets from the invigilator.

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.

:Download Question Paper

: https://www.pdfquestion.in/uploads/INPhO2018.pdfINJSO QP

: https://www.pdfquestion.in/uploads/INPhO2018-So.pdfSolutions

## Model Questions

** Date**: 28 January 2018

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

__Time__**: 75**

__Maximum Marks__** Questions & Summary Answers **:

1. In a nucleus, the attractive central potential which binds the proton and the neutron is called [4]

the Yukawa potential. The associated potential energy U(r) is U(r) = – e-r/ r

Here = 1.431 fm (fm = 10-15 m), r is the distance between nucleons, and = 86.55MeV·fm is the nuclear force constant (1MeV = 1.60×10-13 J). Assume nuclear force constant to be A~c. Here ~ = h/2 and h is Planck’s constant. In order to compare the nuclear force to other fundamental forces of nature within the nucleus of Deuterium (2H), let the constants associated with the electrostatic force and the gravitational force to be equal to B~c and C~c respectively. Here A,B and C are dimensionless. State the expression and numerical values of A,B and C.

2. An opaque sphere of radius R lies on a horizontal plane. On the perpendicular through the point of contact, there is a point source of light at a distance R above the top of the sphere (i.e. 3R from the plane).

a. A transparent liquid of refractive index [6] p3 is filled above the plane such that the sphere is just covered with liquid. Find the area of the shadow of the sphere on the plane now.

3. Consider an infinite ladder of resistors. The input current I0 is indicated in the figure.

(a) Find the equivalent resistance of the ladder.

(b) Find the recursion relation obeyed by the currents through the horizontal resistors r. You [2] will get a relationship where In will be related to (may be several) Iis, i < n, n > 0.

(c) Solve this for the special case R = r to obtain In [4] and I0 n as explicit functions of n. You may have to make a reasonable assumption about the behaviour of In as n becomes large.

(d) If the ladder is chopped off after the N-th node (so that IN+1 = 0) what will the form of [4]

4. An hour glass is placed on a weighing scale. Initially all the sand [9] of mass m0 kg in the glass is held in the upper reservoir (ABC) and the mass of the glass alone is M kg. At t = 0, the sand is released. It exits the upper reservoir at constant rate dm dt = kg/s

where m is the mass of the sand in the upper reservoir at time t sec. Assume that the speed of the falling sand is zero at theneck of the glass and after it falls through a constant height h it instantaneously comes to rest on the floor (DE) of the hour glass. Obtain the reading on the scale for all times t > 0. Make a detailed plot of the reading vs Time.

5. (a) Consider two short identical magnets each of mass M and each of which maybe considered [3] as point dipoles of magnetic moment ~µ. One of them is fixed to the floor with its magnetic oment pointing upwards and the other one is free and found to float in equilibrium at a height z above the fixed dipole. The magnetic field due to a point dipole at a distance r from it is Obtain an expression for the magnitude of the dipole moment of the magnet in terms of z and related Quantities.

i. Consider a ring of mass Mr [11/2] rotating with uniform angular speed about its axis. A charge q is smeared uniformly over it. Relate its angular momentum ~ Sr to its magnetic moment

ii. Assume that the electron is a sphere of uniform charge density rotating about its diam- [1] eter with constant angular speed. Also assume that the same relation as in the previous part holds between its angular momentum ~S and its magnetic dipole moment (~µB). Further assume that S = h/(2) where h is Planck’s constant. Calculate µB.

iii. Assume that the sole contribution to the dipole moment of a ZnFe2O4 molecule comes [3] from an unpaired electron. Also assume that the magnets in the part (5a) are 0.482 kg each of ZnFe2O4 and the unpaired electrons of the molecules are all aligned. Calculate the height z. (Note: The molecular weight of ZnFe2O4 = 211)

iv. In an experiment µB [11/2] is aligned along a magnetic field of 1 T. It is flipped in a direction anti-parallel to the magnetic field by an incident photon. What should be the wavelength of this photon?

** 6. The Van der Waals Gas**:

Consider n mole of a non-ideal (realistic) gas. Its equation of state maybe described by the Van der Waals equation where a and b are positive constants. We take one mole of the gas (n = 1). You must bear in mind that one is often required to make judicious approximations to understand realistic systems.

(a) For this part only take a = 0. Obtain expressions in terms of V , T and constants for

i. the coefficient of volume expansion ();

ii. the isothermal compressibility

ii. Obtain the values of a and b for CO2 given Tc [1] = 3.04×102 K and Pc = 7.30 ×106 N·m-2.

iii. The constant b represents the volume of the gas molecules of the system. Estimate the [1] size d of a CO2 molecule.

** (c) The gas phase **:

For the gaseous phase the volume VG b. Let the pressure PLG = P0, the saturated vapour pressure.

i. Obtain the expression for VG [11/2] in terms of R, T, P0 and a.

ii. State the corresponding expression for VI [1/2] for an ideal gas. VI =

iii. Obtain (VG -VI [2] )/VI for water given T = 1.00 ×102 C, P0 = 1.00×105 Pa, b = 3.10 × 10 -5 m3·mol-1 and a = 0.56 m6·Pa·mol-2. Comment on your result.

** (d) The liquid phase**:

For the liquid phase P a/V 2 L.

i. Obtain the expression for VL [11/2] .

ii. Obtain the density of water (w [11/2] ). You may take the molar mass to be 1.80 × 10-2 kg·mole-1. w =

iii. The heat of vaporization is the energy required to overcome the attractive intermolecular [2] force as the system is taken from the liquid phase (VL) to the gaseous phase (VG). The term a/V 2 represents this. Obtain the expression for the specific heat of vaporization per unit mass (L) and obtain its value for water.

7. A small circular hole of diameter d is punched on the side and the near the bottom of a transparent cylinder of diameter D. The hole is initially sealed and the cylinder is filled with water of density w. It is then inverted onto a bucket filled to the brim with water. The seal is removed, air rushes in and height h(t) of the water level (as measured from the surface level of the water in the bucket) is recorded at different times (t). The figure below and the table in part

(c) illustrates this process. Assume that air is an incompressible fluid with density a and its motion into the cylinder is a streamline flow. Thus its speed v is related to the pressure difference P by the Bernoulli relation. Take the outside pressure P0 to be atmospheric pressure = 1.00 × 105 Pa.

(a) Obtain the dependence of the instantaneous speed vw [3] of the water level in the cylinder on

(b) Obtain the dependence of h on time.

(c) The table gives the height h as function of time [4] t. Draw a suitable linear graph (t on x axis) from this data on the graph paper provided. Two graph papers are provided with this booklet in case you make a mistake.