OLYMPI OLYMPIAD AD PREPARATORY PREPARATORY TEST-3 (OPT-3) (OPT-3) STAGE-I SUBJECT : PHYSICS Date : 06-11-2014
Time : 2 Hrs.
Max. Marks : 240
Instruction to candidates candidate s (as had been there in the past NSEP papers) 1.
In addition to this question paper, you are given answer sheet for part A and an answer paper for part B.
2.
On the answer sheet for part A, fill up all the entries carefully in the space provided, ONLY In BLOCK CAPITALS. Incomplete / incorrect / carelessly filled information may disqualify your candidature.
3.
On part A answer sheet, use only BLUE or BLACK BALL PEN for making entries and marking answers.
4.
Part A has two parts. In part A1 (Q.No. 1 to 40) each question has Four alternatives, alternatives, out of which only one is correct. Choose the correct alternative altern ative and mark a cross (X) in the corresponding box on the answer sheet. For example,
Part A2 (Q.Nos. 41 to 50) has four alternatives in each question, but any number of these (4, 3, 2, or 1) may be correct. You have to mark ALL correct alternatives and mark a cross (X) for each, like
5.
For Part A1, each correct answer gets 3 marks; wrong answer gets a penalty of 1 mark. For Part A2 full marks are 6 for each question, you get them when ALL correct answer only are marked.
6.
Any rough work should be done only on the sheets provided with part B answer paper.
7.
Use of nonprogrammable nonprogrammable calculator calculator is allowed.
8.
No candidate should leave the examination hall before the completion of the examination.
9.
After submitting s ubmitting your answerpapers, answerpa pers, read r ead the instructions regarding evaluation ev aluation given at the end of the question paper. PLEASE DO NOT MAKE ANY MARKS MARKS OTHER THAN (X) IN THE SPACE SPACE PROVIDED ON THE ANSWER SHEET OF PART A.
Answer sheets are evaluated with the help of a machine. Hence, CHANGE OF ENTRY IS NOT ALLOWED. Scratching or overwriting may result in wrong score. DO NOT WRITE ANYTHING ON THE BACK BACK SIDE OF PART PART A ANSWER SHEET. SHEET. EVALUATION EVALUATION PROCEDURE PROCEDU RE (NSEP) : 10.
Part ’A’ Answers of ALL the candidates are examined .
11.
Part B is evaluated of only those students who get marks above a certain "cut off"marks off"marks in Part A. (e.g. NSEP Total marks for Part A are 180. Students getting (say)100 or more than 100 marks in Part A are identified and their Part B is evaluated.Thus "cut off" marks are 100 in this example.)
12.
PART B IS NOT EVALUATED OF ALL THE CANDIDATES.
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PART A
MARKS = 120
SUB-PART A – 1 : ONLY ONE OUT OF FOUR OPTIONS IS CORRECT Sub-Part A-1 (120 Marks) In questions 1 to 40 any one of options (A, B, C or D) is correct. You have to mark the most appropriate of them correctly to get 3 marks. If marked answer is wrong you get -1 score. There is no negative marking if you do not attempt the question.
1.
A 2F capacitor is initially charged to 20 Volts and then shorted across a 8 H inductor. The maximum value of the current in the circuit is : (A) 10.0 A (B) 7.5 A (C) 12.0 A (D) 8.2 A
2.
Resistors each of value 1 are arranged as shown in the figure. The equivalent resistance between point A and B is :
(A) 3.
1 2
(B)
1 5
(C)
5 4
(D) None of these
Two metallic bodies separated by a distance 20 cm, are given equal and oppos ite charges of magnitude 0.88 C . The component of electric field along the line AB, between the plates, varies as E x= 3 x2 + 0.4 N/C, where x (in meters) is the distance from one body towards the other body as shown. C A
x
B 20 cm
(A) The capacitance of the system is 20F (B) The capacitance of the system is 30F (C) The potential difference between A and C is 0.088 Volt. (D) The potential difference between A and C cannot be determined from the given data. 4.
An electron passes between two parallel plates of a capacitor as shown in the diagram.The electron enters between the plates at t=0 and it comes out of the plates at time t=T .The electron hits the screen at A,as shown.Now a time varying potential difference V is applied between the plates,as shown in the graph. (Neglect the gravity) .The point where the electron now will strike the screen (as compared to point A) will be V V electron
0
A
n e e r c S
e g a t l o V
T
(A) Deflected up (C) Deflected up then down
(B) Deflected down (D) Deflected down then up
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5.
A positive point charge Q is placed (on the axis of disc )at a distance of 4R above the centre of a disc of radius R. The magnitude of electric flux through the disc is . Now a hemispherical shell of radius R is placed over the disc such that it forms a closed surface. The flux through the curved surface taking direction of area vector along outward normal as positive, is
(B)
(A) zero
(C) –
(D) 2
6.
A long straight wire is carrying current I 1 in + z direction. The x – y plane contains a closed circular loop carrying current I 2 and not encircling the straight wire. The force on the loop will be : (A) µ0I 1I 2/2 (B) µ0I 1I 2/4 (C) zero (D) depends on the distance of the centre of the loop from the wire.
7.
A uniform electric field E in the y direction and uniform magnetic field B in the x direction exists in free space. A particle of mass m and carrying charge q is projected from the origin with speed v 0 along the y axis. The speed of particle as a function of its y co-ordinate will be
(A)
2
v0
2qEy m
(B)
2
v0
4qEy m
(C) v02
qEy m
(D) v 0
8.
The ratio of final root mean square velocity to initial root mean square velocity of nitrogen molecules if nitrogen gas is compressed adiabatically from a pressure of one atmosphere to a pressure of two atmosphere is : (A) 22/7 (B) 21/7 (C) 21/5 (D) 22/5
9.
In a certain polytropic process the volume of the diatomic gas was increased 4 times simultaneously the pressure decreased 8 times. The molar heat capacity of the gas in J/mole K in nearest integer for this process is : (Take R = 8.13 J/mole K). (A) 2 (B) 4 (C) 6 (D) 8
10.
The ratio of translational and rotatio nal kinetic energies at 100 K temperature is 3 : 2. Then the internal energy of one mole gas at that temperature is[R = 8.3 J/mol-K] (A) 1175J (B) 1037.5 J (C) 2075 J (D) 4150J
11.
Two simple pendulum of length 100cm and 121cm length start s winging together. (Note : Swing together means same phase) (A) they will swing together again when the pendulum of l ength 100cm makes 10 oscillations (B) they will swing together again when the pendulum of l ength 121cm makes 11 oscillations (C) they will swing together again when the pendulum of length 100cm makes 11 oscillations (D) they will swing together again when the pendulum of length 121cm makes 12 oscillations
12.
A metre stick swinging in vertical plane about a fixed hori zontal axis passing through its one end undergoes small oscillation of frequency f 0. If the bottom half of the s tick were cut off, then its new frequency of small oscillation would become:
(A) f 0
(B)
2 f 0
(C) 2f 0
(D) 2 2 f 0
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13.
A plano-convex lens has curved surface having radius of curvature 60 cm and it is made of material of refractive index 1.5. When the convex surface is silvered , the system will work as a concave mirror of focal length. (A) 20 cm (B) 24 cm (C) 30 cm (D) 15 cm
14.
A thin symmetrical double convex lens of refractive index 2 = 1.5 is placed between a medium of refractive index 1 = 1.4 to the left and another medium of refractive index 3 = 1.6 to the right. Then, the system behaves as : (A) a convex lens (B) a concave lens (C) a glass plate (D) a convexoconcave lens
15.
A ray of light falls on a transparent sphere with centre at C as shown in the figure. The ray emerges from the sphere parallel to the line AB. The refractive index of the sphere is :
(A) 16.
(B)
2
2 m (B) 5 1 4 cos 2
2 m (C) 9 1 8 cos 2
M1 R (B) M M < 2 r 1 2
A particle is projected with a velocity
1 2
2 m (D) 9 8 cos 2
(C) M1R2 < M2R1
(D) M1R2 > M2 R1
4gR
vertically upward from the surface of the earth, R being the 3 radius of the earth & g being the acceleration due to gravity on the surface of the earth. The velocity of the particle when it is at half the maximum height reached by it is : (A)
19.
(D)
The earth has mass M1 and radius R1. Similarly the sun has mass M2 and radius R2. Distance between their centre is r. It is known that the centre of mass of the earth-sun system lies well within the sun. Therefore, M1 R (A) M M > 2 r 1 2
18.
3 2
In Young’s double slit experiment, one of the slits is wider than the other, so that the amplitude of the light from one slit is double that from the other slit. If m be the maximum intensity, the resultant intensity when they interfere at phase difference is given by : 2 m (A) 3 1 2 cos 2
17.
(C)
3
gR 2
(B)
gR
(C)
3
gR
(D)
2gR 3
A cone is hanging inside a liquid of density with the help of string as shown in figure. Height of cone is H and base radius is R . The force due to liquid on slant surface of cone is (Patm = 0) :
H R
(A) gHR 2
(B) HR 2
(C)
4 gHR 2 3
(D)
2 gHR 2 3
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20.
A large tank has two holes in the wall. Hole 1 has a square cross section with side l and is cut at a depth h from the top. Hole 2 has a circular cross section of radius r at a depth of 4h from the top. When the tank is completely filled, the quantities of water flowing out through the holes per second are the same. Then, l is equal to : (A)
21.
r 2
(B) µ < 1
(D) r
(C) µ > 1
(D) µ > 1/2
(B) 10 % of y (D) does not depend on y
(B) 2 sin –1 (2)
(C) tan –1 ()
(D) 2 tan –1 (/2)
The atmospheric pressure on the earths surface is P in MKS units. A table of area 2 m2 is tilted at 45º to the horizontal. The force on the table from one side due to the atmosphere is (in newtons) (A) 2P
25.
The coefficient of friction between the block A of mass m and block B of mass 2m is . There is no friction between block B and the inclined plane. If the system of blocks A and B are released from rest and there is no slipping between A and B, then
(A) 2 cos –1 (2) 24.
r
A hanging rod breaks at 5 % of strain under its own weight. The breaking stress of the material of the rod: ( y young modulus) (A) 5 % of y (C) equal to y
23.
(C)
A cube is resting on an inclined plane. What must be the value of coefficient of friction between cube and plane so that cube may topple before sliding ? (A) µ = 1/2
22.
(B) r 2
(B)
2P
(C) 2 2 P
(D)
P 2
Figure shows a system of two blocks of 10 kg and 5 kg mass, connected by ideal strings pulleys. Here ground is smooth and friction coefficient between the two blocks is µ = 0.5. A horizontal force F is applied on lower block as shown. The minimum value of F required to start sliding between the blocks is : (Tage g = 10 m/s2)
(A) 12.5 N
(B) 25 N
(C) 50 N
(D) 100 N
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26.
A boatman rows in such a direction that he moves perpendicular to a river stream and takes time t 1 to cover some distance. He takes time t 2 to cover the same distance when he rows along the river. If v 1 is the speed of boat in still water and v 2 the speed of the stream, then t 1/t 2 is : v1 v2 v1 v2
(A)
27.
v1 v2 v1 v2 2
(B)
v1 v2
2
(C)
(D)
v1 v2
A ball A of mass 2m moving due east with a speed 8u collides head on with a ball B of mass m. The velocity of B after collision is 5u due east. If the coefficient of restitution is lost is : (A)
28.
112 153
(B)
80 137
(C)
(A) 2
1 , the fraction of the initial 11
41 153
(D)
The centre of mass of two masses m & m moves by distance m is kept fixed. The ratio
29.
v1 v2 v1 v2
kinetic energy
100 121
x when mass m is moved by distance x and 5
m is : m
(B) 4
(C) 1/4
(D) None of these
A particle moving with initial velocity vi = (3i 5 j ) m-s –1, collides with a smooth plane wall placed at ˆ
ˆ
some orientation to the particles trajectory. The resulting velocity of the particle is v f = (2i j ) m-s –1. ˆ
ˆ
The coefficient of restitution for this collision is : (A) 16/33 30.
(B) 5/34
(C) 16/45
(D) 8/45
A large open tank is filled with water upto a height H. A small hole is made at the base of the tank. It takes T1 time to decrease the height of water to
H (n > 1) and it takes T 2 time to take out the remaining water. If n
T1 = T2, then the value of n is : (A) 2
(B) 3
(C) 4
(D) 2 2
31.
The half life of a certain radioactive material ( zX 100) is 6.93 × 106 s. In order to have an activity of 6.0 × 108 disintegrations per second, the amount of material needed is nearly : (A) 10 –9 kg (B) 10 –16 kg (C) 10 –6 kg (D) 10 –4 kg
32.
A photon of wavelength (less than threshold wavelength 0) is incident on a metal surface of workfunction W 0. The minimum de–Broglie wavelength of the ejected electrons of mass m is :
hc (A) h 2m W0
33.
(B)
h
hc W0
m
(C)
h
hc W0
h (D)
2m
hc W0
m
Find the numerical value of DeBroglie wavelength of an electron in the 1st orbit of hydrogen atom assuming Bohrs atomic model. You can use standard values of the constants. Leave your answer i n terms of . (A) 1.058 Å (B) 0.529 Å (C) 0.2116 Å (D) 0.4232 Å Corporate Office : CG Tower, A-46 & 52, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.)-324005 Website : www.resonance.ac.in | E-mail :
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34.
An electron in hydrogen atom after absorbing an energy photons jumps from energy state n 1 to n2. Then it returns to ground state after emitting six different wavelengths in emission spectrum. The energy of emitted photons is either equal to, less than or greater than the absorbed photons. Then n 1 and n2 are : (A) n2 = 4, n1 = 3
35.
3 4
(B) v 3 4
(C) less than v
Dimensions of
h G
(C) [ M L T 2 ]
(D) [ M L2 T 1 ]
(B) [M –2 L 1 T –1]
(C) [M –1 L –2 T –1]
(D) [M0 L0 T0]
A particle is released from rest 10 cm from a large sheet carrying a surface charge density of –2.21 10 –9 C/m2. It will strike the sheet after the time. ( 0 = 8.84 × 10 –12 C2/Nm2) (B) 2 s
(C) 2 2 s
(D) 4 2 s.
If the electric potential of the inner shell is 10 volt & that of the outer shell i s 5 volt, then the potential at the centre will be: (the shells are uniformly charged)
(A) 10 volt 40.
4 3
are : (where h is plank constant)
(A) 4 s 39.
4 3
(D) greater than v
(B) [ M L2 T 2 ]
(A) [M2 L –1 T 1] 38.
(D) n 2 = 4, n 1 = 1
The dimensional formula for latent heat is : (latent heat is heat per unit mass) (A) [ M0 L 2 T 2 ]
37.
(C) n2 = 4, n 1 = 2
In a photoelectric experiment, with light of wavelength , the fastest electron has speed v. If the exciting 3 wavelength is changed to , the speed of the fastest emitted electron will become 4 (A) v
36.
(B) n 2 = 5, n 1 = 3
(B) 5 volt
(C) 15 volt
(D) 0
An electron (charge e, mass ’ m ’ ) is revolving around a fixed proton in circular path of radius ’ r ’. The magnetic field at the centre due to electron is: (A) 0
(C)
0 e 8 r m0 r
(B)
(D)
0 8
e
2
r 2 m0 r
0 e 2 4 r m0 r
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Sub-Part A-2 (60 Marks) In questions 41 to 50 any number of options (A, B, C or all D) may be correct. You have to mark all of them correctly to get 6 marks. Even if one marked answer is wrong, or one right answer is missed, you get zero score. There is no negative marking here : 41.
Graph shows variation of source emf V and current i in a series RLC circuit, with time.
V/i
V i
t
(A) The current leads the emf in the circuit. (B) The circuit is more inductive than capacitive. (C) To increase the rate at which energy is transferred to the resistive load, L should be decreased. (D) To increase the rate at which energy is transferred to the resistive load, C should be increased. 42.
The galvanometer shown in the figure has resistance 10 .It is shunted by a series combination of a resistance S = 1 and an ideal cell of emf 2V. A current 2A passes as shown. G=10
2A
S=1
2V
(A) The reading of the galvanometer is 1A (B) The reading of the galvanometer is zero (C) The potential difference across the resistance S is 1.5 V (D) The potential difference across the resistance S is 2 V 43.
Two long conducting wires carrying eq ual currents are placed parallel to the z-axi s. A charged particle is made to move in a circular path of radius a with centre of the path at point (0, 2a) in clockwise direction. During the course of motion, it passes throu gh four points P, Q, R and S having coordinates (0, a), (–a, 2a), (0, 3a) and (a, 2a) respectively. The magnitude of force exerted on the particle by the magnetic field created by the wires is maximum when it passes through point. y (0,2a)
(-a,0)
(A) P 44.
(B) Q
0
x (a,0)
(C) R
(D) S
In case of hydrogen and oxygen at NTP, which of the following quantities is/are the same ? (A) Average of magnitude of momentum per molecule (B) Average kinetic energy per molecule (C) Kinetic energy per unit volume (D) Kinetic energy per unit mass Corporate Office : CG Tower, A-46 & 52, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.)-324005 Website : www.resonance.ac.in | E-mail :
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45.
One mole of an ideal gas with = 1.5 starts at point A, where its volume and pressure are 1.00 m 3 and 250 kPa, respectively. It then undergoes adiabatic expansion upto 4 times of its volume, ending at point B. It is then heated at constant volume to point C, and then compressed back to A isothermally :
(A) the pressure at point B is 125 kPa (B) the pressure at point B is 31.25 kPa (C) ratio of magnitude of change in internal energy along process BC to process AB is 1 (D) ratio of magnitude of change in internal energy along process BC to process AC is infinite 46.
A particle of mass 1kg is moving in the x–y plane and its potential energy U in joule obeys the law U = 6x + 8y, where (x,y) are the coordinates of the particle in meter. If the particle starts from rest at (9,3) at time t = 0, then : (A) Magnitude of acceleration of particle is 10 m/s2 (B) Acceleration of particle is zero (C) The particle crosses the y–axes at time t =
3 sec.
(D) The speed of the particle when it crosses y–axes is 10 3 m/s 47.
Two artificial satellites of the same mass are moving around the earth in circular orbits of different radii. In comparison to the satellite with lesser orbital radius, the other satellite with higher orbital radius will have : (A) greater kinetic energy. (B) greater potential energy. (C) greater total energy (D) greater magnitude of angular momentum, about the centre of the circular orbit.
48.
A light rigid rod AOB bent at right angles can freely rotate about OB which is vertical. A bug P is at A o. The bug crawls along the rod towards ‘O. Then during the motion: (A) K.E. of the bug decreases (B) angular velocity decreases (C) angular momentum remains constant. (D) both the angular velocity and K.E. of the bug increases. a
49.
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Two points A and B move with speeds v and 2v in two concentric circles with centre O and radii 2r and r respectively. If the points move in the same sense and if OAB = , when the relative motion is along AB, find the value of .
1 (A) sin 5 –1
(C) sin –1 50.
t
1 2
(B) sin
–1
1 3
(D) 60°
When two blocks connected by a stretched mass less spring (as shown) start moving from rest towards each other under mutual interaction. Then (pickup the correct alternative or alternatives) (A) their velocities are equal and opposite. (B) their accelerations are equal and opposite. (C) the force acting on them are equal and opposite. (D) their momentum are equal and opposite Corporate Office : CG Tower, A-46 & 52, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.)-324005 Website : www.resonance.ac.in | E-mail :
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PART B :
MARKS : 60
ALL QUESTIONS ARE COMPULSORY.
ALL QUESTIONS CARRY EQUAL MARKS.
51.
The resistance of uniform wire AB is 9. Find the resistance of part BC for which galvanometer G will show zero deflection.
52.
A constant force in applied perpendicular to rod as shown. If the rod is having a resistance 10 but rails zero resistance then maximum speed (in m/s) of rod is : (rails are very long and frictionless and magnetic field is 10 tesla)
53.
Consider flow of heat from an inner sphere of radius a at temperature T1 to an outer concentric sphere of radius b at temperature T2 through an insultating material filled in between th two spherees. Obtain expressions for the total heat current H and the temperature T at a distance r from the centre, when a steady state is reached.
54.
A is a thin walled sphere at rest made up of glass. The radius of the sphere is 1m and it is filled with a transparent liquid of refractive index S is the luminous source moving directly towards a plane vertical mirror M. A fish in the liquid is moving towards S. The eye of the fish and S are collinear & perpendicular to mirror M. At the moment S is 3m away from the centre of the sphere fish observes that image of S due to reflection is moving with speed of 13m/s. If speed of the fish relative to the sphere is 10m/s and = 1.5 then find the speed (in m/s) of the source at that instant. The system is placed in air.
55.
Starting at rest, a 5 kg object is acted upon by only one force as indicated in figure. Find the total work done by the force. force(N)
20 0
1
2
3
Time (in sec.)
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