Resonance Physics

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(JEE ADVANCED PATTERN)

TARGET : JEE (MAIN+ADVANCED) 2016

COURSE : VIJAY (JR)

SUBJECT : PHYSICS

P06A-15

Date : 27-12-2015

Time: 2 Hours

Maximum Marks : 168

Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.

GENERAL %

1. The sealed booklet is your Question Paper. Do not break the seal till you are instructed to do so. 2. The question paper CODE is printed on the right hand top corner of this sheet.

3. Use the Optical Response Sheet (ORS) provided separately for answering the question. 4. Blank spaces are provided within this booklet for rough work.

5. Write your Name and Roll Number in the space provided on the below cover.

6. After the open booklet, verify that the booklet contains all the 44 questions along with the options are legible.

QUESTION PAPER FORMAT AND MARKING SCHEME :

7. This questions paper consists of Five sections.

8. Carefully read the instructions given at the beginning of each section. 9. Section 1 contains 10 multiple Choice question with Only one correct option.

Marking scheme: +4 for correct answer, 0 if not attempted and –2 in all other cases.

10. Section 2 contains 14 multiple Choice question with one or more than one correct option.

11. Section 3 contains 3 "paragraph" type questions. Each paragraph describes an experiment, a situation or a problem. Two multiple choice questions will be asked based on this paragraph. One or more than one correct option.

12. Section 4 contains 2 "match the following" type question and you will have to match entries in Column I with the entries in Column-II.

Marking scheme : for each entry in Column I, +2 for correct answer, 0 if not attempted and –1 in all other cases.

13. Section 5 contains 12 questions. The answer to each question is a single digit integer ranging from 0 to 9 (both inclusive).

There are 12 Questions & you have to attempt any 8 Questions. If a student attempts more than 8 questions, then only first 8 questions which he has attempted will be checked.

OPTICAL RESPONSE SHEET :

14. Darken the appropriate bubbles on the original by applying sufficient pressure.

15. The original is machine-gradable and will be collected by the invigilator at the end of the examination. 16. Do not tamper with or mutilate the ORS.

17. Write your name, roll number and the name of the examination centre and sign with pen in the space provided for this purpose on the original. Do not write any of these details anywhere else. Darken the appropriate bubble under each digit of your roll number.

DARKENING THE BUBBLES ON THE ORS :

18. Use a BLACK BALL POINT to darken the bubbles in the upper sheet. 19. Darken the bubble COMPLETELY.

20. Darken the bubble ONLY if you are sure of the answer. 21. The correct way of darkening a bubble is as shown here : 22. There is NO way to erase or "un-darkened bubble.

23. The marking scheme given at the beginning of each section gives details of how darkened and not darkened bubbles are evaluated.

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NAME OF THE CANDIDATE : ………..………

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I have read all the instructions I have verified the identity, name and roll number and shall abide by them of the candidate.

- - - - - - Signature of the Candidate Signature of the Invigilator

D O N O T B R E A K T H E S E A L W IT H O U T B E IN G IN S T R U C T E D T O D O S O B Y T H E I N V IG IL A T O R

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Space for Rough Work

Corporate Office : CG Tower, A-46 & 52, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.)- 324005 Website : www.resonance.ac.in | E-mail : [email protected]

Toll Free : 1800 200 2244 | 1800 258 5555 | CIN: U80302RJ2007PLC024029 JRPT4271215C0-1

PHYSICS

SECTION

–

1 : (Maximum Marks : 40)

 This section contains

TEN

questions

 Each question has

FOUR

options (A), (B), (C) and (D).

ONLY ONE

of these four option is correct

 For each question, darken the bubble corresponding to the correct option in the ORS  Marking scheme :

+4 If only the bubble corresponding to the correct option is darkened 0 If none of the bubble is darkened

–2 In all other cases

1. A particle is executing SHM according to the equation x = A cos t. Average speed of the particle during the interval 0 t 

6   . (A) 3A 2  (B) 3A 4  (C) 3A  (D) 3A 





2 3

2. A transverse wave is propagating along +x direction. At t = 2 sec, the particle at x = 4m is at y = 2 mm. With the passage of time its y coordinate increases and reaches to a maximum of 4 mm. The wave equation is(using  and k with their usual meanings)

(A) y 4 sin[ (t 2) k(x 2) ] 6        (B) y 4 sin [ (t 2) k(x) ] 6       (C) y 4 sin [ (t 2) k(x 4) 5 ] 6        (D) y 4 sin [ (t 2) k(x 4) ] 6       

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Toll Free : 1800 200 2244 | 1800 258 5555 | CIN: U80302RJ2007PLC024029 JRPT4271215C0-2 3. A student is performing the experiment of Resonance Column. The diameter of the column tube is

4cm. The frequency of the tuning fork is 512 Hz. The air temperature is 38° C in which the speed of sound is 336 m/s. The zero of the meter scale coincides with the top end of the Resonance Column tube. When the first resonance occurs, the reading of the water level in the column is (A) 14.0 cm (B) 15.2 cm (C) 16.4 cm (D) 17.6 cm

4. A stationary observer receives sonic oscillations from two tuning forks, one of which approaches and the other recedes with same speed. As this takes place the observer hears the beat frequency of 2 Hz. Find the speed of each tuning fork, if their oscillation frequency is 680 Hz and the velocity of sound in air is 340 m/s. [Use g = 10 m/s2_]

(A) 1 m/s (B) 2 m/s (C) 0.5 m/s (D) 1.5 m/s

5. Seven identical disc are arranged in a hexagonal, planar pattern so as to touch each neighbor, as shown in the figure. Each disc has mass m and radius r. What is the moment of inertia of the system of seven disks about an axis passing through the centre of central disk and normal to plane of all disks ? (A) 7 2mr 2 _(B)13 2 mr 2 _(C)29 2 mr 2 _(D)55 2 mr 2

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Toll Free : 1800 200 2244 | 1800 258 5555 | CIN: U80302RJ2007PLC024029 JRPT4271215C0-3 6. Assuming frictionless contacts, then the magnitude of external horizontal force P applied at the

lower end for equilibrium of the rod will be : (The rod is uniform and its mass is 'm'):

(A) mg 2 (B) mg 2 cot  (C) mg 2 tan  (D) mg 2 sec  

7. A massless stick of length L is hinged at one end and a mass m attached to its other end. The stick is free to rotate in vertical plane about an fixed horizontal axis passing through frictionless hinge. The stick is held in a horizontal position. At what distance x from the hinge should a second mass M = m be attached to the stick, so that stick falls as fast as possible when released from rest

(A) 2L (B) 3L (C) ( 21)L (D) ( 31)L

8. A particle executes SHM in a straight line. In the first second starting from rest it travels 'a' distance a and in the next second a distance 'b' in the same direction. The amplitude of S.H.M will be (A)

2 2a 3ab

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Toll Free : 1800 200 2244 | 1800 258 5555 | CIN: U80302RJ2007PLC024029 JRPT4271215C0-4 9. A particle is moving with velocity _v_ˆ_i__{3 j}ˆ_{and it produces an electric field at a point given by}

ˆ E2k



. It will produce magnetic field at that point equal to (all quantities are in S.. units and speed of light is c) (A)6iˆ ₂2 jˆ c  (B) 6iˆ ₂2 jˆ c 

(C) zero (D) can not be determined from the given data

10. If the magnetic field at 'P' can be written as K tan 2        then K is : (A) 0 4 d    (B) 0 2 d    (C) 0 d    (D) 2 0 d   

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SECTION

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2 : (Maximum Marks : 56)



FOURTEEN

questions

 Each question has

FOUR

ONE OR MORE THAN ONE

of these four option(s) is(are) correct

 For each question, darken the bubble(s) corresponding to all the correct option(s) in the ORS  Marking scheme :

+4 If only the bubble(s) corresponding to all the correct option(s) is(are) darkened 0 If none of the bubbles is darkened

11. A rod of length 0.3 m having variable linear mass density from A to B as  = 0x(x is distance from A in meter), where 0 = 100 kg/m

2_{is suspended by two light wires of same length. Ratio of their} linear mass density is 2 : 9. Then which of the following is/are correct :

(A) Ratio of wave speed in wire–1 to wire–2 is 3 : 2 (B) Ratio of wave speed in wire–1 to wire–2 is 3 : 1

(C) Second harmonic in wire–1 has same frequency as third harmonic in wire–2 (D) Third overtone in wire–1 has same frequency as fifth overtone in wire–2

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Toll Free : 1800 200 2244 | 1800 258 5555 | CIN: U80302RJ2007PLC024029 JRPT4271215C0-6 12. y-x curve at an instant for a wave travelling along x axis on a string is shown. Slope at the point A

on the curve, as shown, is 53°.

53°

A y

x

(A) Transverse velocity of the particle at point A is positive if the wave is travelling along positive x axis.

(B) Transverse velocity of the particle at point A is positive if the wave is travelling along negative x axis.

(C) Magnitude of transverse velocity of the particle at point A is greater than wave speed. (D) Magnitude of transverse velocity of the particle at point A is lesser than wave speed.

13. A particle is moving along x-axis. Its position 'x' varies with time 't' as follows x = A + A(1 – cost)

Then select the correct alternatives :

(A) particle is doing SHM between point x = 2A and x = A (B) the speed of particle is maximum at x = 2A

(C) time taken by particle from x = A to directly x = 3A is  

(D) time taken by particle from x= A to directly x = 2A is 2

 

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Toll Free : 1800 200 2244 | 1800 258 5555 | CIN: U80302RJ2007PLC024029 JRPT4271215C0-7 14. Consider a spring that exerts the following restoring force :

F = –kx for x > 0 F = –4kx for x < 0

A mass m on a frictionless surface is attached to the spring displaced to x = A by stretching the spring and released :

(A) The period of motion will be T = 3 m 2 k

(B) The most negative value of x the mass m can reach will be x = A 2 

(C) The time taken to move from x = A to x = A 2

 , straight away will be equal to 5 m 8 k



(D) The total energy of oscillations will be 5 2 kA

2

15. A block of mass m = 1 kg is placed on a smooth surface and is connected with a spring of spring constant k = 100 N/m and another end of spring is connected to a fixed wall as shown. The block is pulled by a distance A = 0.10 m from its natural length and released at t = 0.

(A) The maximum speed is after t =

20 

s. (B) Time taken to cover first 0.10 m, t = 20

 s. (C) Time taken to cover first 0.05 m, t =

40 

s. (D) Time taken to cover first 0.05 m, t = 30

 s.

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Toll Free : 1800 200 2244 | 1800 258 5555 | CIN: U80302RJ2007PLC024029 JRPT4271215C0-8 16. A particle performing S.H.M. undergoes displacement of A

2 (where A = amplitude of S.H.M.) in one second. At t = 0 the particle was located at either extreme position or mean position. The time period of S.H.M. can be : (consider all possible cases)

(A) 12s (B) 2.4 (C) 6s (D) 1.2s

17. A wave pulse moving to the right along the x-axis is represented by the wave function y(x, t) = 2.0 ₂

(x3.0 t) 1

, where x and y are in centimeters and t is in seconds. (The maximum pulse height is defined as maximum displacement along y-axis). Then

(A) The maximum pulse height is decreasing with time. (B) The maximum pulse height is constant with time (C) The speed of the pulse is 3.0 cm/s

(D) The speed of the pulse is 0.33 cm/s

18. In a standing transverse wave on a string :

(A) In one time period all the particles are simultaneously at rest twice.

(B) All the particles must be at their positive extremes simultaneously once in one time period. (C) All the particles may be at their positive extremes simultaneously once in a time period. (D) All the particles are never at rest simultaneously.

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Toll Free : 1800 200 2244 | 1800 258 5555 | CIN: U80302RJ2007PLC024029 JRPT4271215C0-9 19. A source emit sound waves of frequency 1000 Hz. The source moves to the right with a speed of

32 m/s relative to ground. On the right a reflecting surface moves towards left with a speed of 64 m/s relative to ground. The speed of sound in air is 332 m/s :

(A) wavelength of sound ahead of source is 0.3 m

(B) number of waves arriving per second which meets the reflected surface is 1320 (C) speed of reflected wave is 268 m/s

(D) wavelength of reflected waves is nearly 0.2 m

20. An air column in a pipe closed at one end is made to vibrate in its second overtone by a tuning fork of frequency 440 Hz. The speed of sound wave in air is 330 m/s. End corrections may be neglected. Let P₀ denote the mean pressure at any point in the pipe, and P0 the maximum amplitude of pressure variation. Then :

(A) length of the pipe is 15 16m (B) length of the pipe is 9

16m

(C) the maximum pressure at the open end is P₀ (D) the minimum pressure at the open end is P₀

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Toll Free : 1800 200 2244 | 1800 258 5555 | CIN: U80302RJ2007PLC024029 JRPT4271215C0-10 Space for Rough Work

c

observer following the car with speed v₀. The speed of sound in air is v. (A) the wavelength of sound reaching the hill is v

f (B) the wavelength of sound reaching the hill is v vc

f 

(C) The wavelength of sound of horn directly reaching the observer is v vc f 

(D) the beat frequency observed by the observer is c



o



2 2 c 2 v v v f v v  

22. A uniform solid cylinder of mass m, radius R is at rest on an extremely rough horizontal surface. Now a force F = kt where k = constant and t = time, is applied at the highest point on the cylinder. Assume that the cylinder is not slidding at all.

(A) The friction force acting on the cylinder varies with time as

(B) Velocity of the highest point after time t will be 2 2kt

3m (C) Velocity of the highest point after time t will be

2 4kt

3m

(D) If the coefficient of friction between the ground and the cylinder is , the cylinder will start slidding at t 3 mg

k 

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23. A rigid equilateral triangular frame made of three identical thin rods (mass = m & length = ) is free to rotate smoothly in vertical plane. Frame is hinged at one of its vertices H. Frame is released from rest from the position shown in figure then select correct atternative (s).

(A) Net initial torque about point H is 3

2mg (B) Initial angular acceleration of the frame is g/ (C) Initial force of hinge on the frame is 3 mg (D) Initial force of hinge on the frame is 3 mg

24. A thin rod of mass m and length  is free to rotate on a smooth horizontal plane about its one fixed end. When it is at rest, it receives a horizontal impulse J at its other end, at angle of 37º with the length. Immediately after impact :

(A) Angular momentum of the rod is 0.6 J (B) Angular velocity of the rod is 1.8J

m (C) Kinetic energy of the rod is

2 0.54J

m

(D) Linear velocity of the centre of mass of the rod is 9 10

J m

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SECTION

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3 : (Maximum Marks : 24)

THREE

paragraphs

 Based on each paragraph, there will be

TWO

questions.

 Each question has

FOUR

ONE OR MORE THAN ONE

of these four option(s) is(are) correct 

 For each question, darken the bubble(s) corresponding to all the correct option(s) in the ORS  Marking scheme :

+4 If only the bubble(s) corresponding to all the correct option(s) is(are) darkened 0 If none of the bubbles is darkened

Paragraph for Question Nos. 25 to 26

A block of mass m is attached to an unstretched ideal spring of force constant k and held at rest. A bullet of mass m/2 is vertically fired to it with speed u = 4 3 g m

k as shown. The moment bullet

SECTION

–

4 : (Maximum Marks : 16)

Column

II

 The ORS contains a 4 × 4 matrix whose layout will be similar to the one shown below :

(A) (B) (C) (D)

 For each entry in

Column

I

, darken the bubbles of all the matching entries. For example, if entry (A) in

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SECTION

–

5 : (Maximum Marks : 32)

TWELVE

questions

 There are 12 Questions & you have to attempt any 8 Questions. If a student attempts more than 8 questions, then only first 8 questions which he has attempted will be checked.

 The answer to each question is a

SINGLE DIGIT INTEGER

ranging from 0 to 9, both inclusive  For each question, darken the bubble corresponding to the correct integer in the ORS

 Marking scheme :

+4 If the bubble corresponding to the answer is darkened 0 If none of the bubbles is darkened

33. A particle is executing SHM on a straight line. A and B are two points at which its velocity is zero. It passes through a certain point P (AP<PB) at successive intervals of 0.5 and 1.5 sec with a speed of 3 2 m/s. Determine the maximum speed (in m/s)

34. A nonuniform string of mass 45 kg and length 1.5 m has a variable linear mass density given by = kx, where x is the distance from one end of the string and k is a constant. Tension in the string is 15 N which is uniform. Find the time (in second) required for a pulse generated at one end of the string to travel to the other end

35. A source of sound of frequency 1.8 kHz moves uniformly along a straight line at a distance 250 m from observer. The velocity of source is 0.8 C where C is the velocity of sound. Find out the frequency of sound received by observer (in kHz) at the moment when the source gets closest to him.

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Toll Free : 1800 200 2244 | 1800 258 5555 | CIN: U80302RJ2007PLC024029 JRPT4271215C0-19 36. A uniform square plate of mass m = 100 gm and side a = 24 cm can rotate about a smooth vertical

axis passing through one edge. It is initially at rest. A particle of mass m = 100 gm is moving horizontally and perpendicular to the plane of the plate with velocity u = 70 cm/s. It collides with the plate elastically at the centre of the plate. Find the angular velocity (in rad/s) of the plate just after collision ?

S

Toll Free : 1800 200 2244 | 1800 258 5555 | CIN: U80302RJ2007PLC024029 JRPT4271215C0-22 a = 2m about the axis AB which is in the plane of sheet :

44. In the figure shown strings AB and BC have masses m and 2m respectively. Both are of same length . Mass of each string is uniformly distributed on its length. The string is suspended vertically from the ceiling of a room. A small jerk wave pulse is given at the end 'C'. It goes up to upper end 'A' in time 't'. If m = 2 kg,  =

9610

1681m, g = 10 m/s

2_, _{2 = 1.4, 3 = 1.7 then find the}

value of 't' (in seconds) in nearest integer.

A

B

C

2m,

m,