3-Simple Harmonic Motion AND WAVES

PART TEST - 1 (PT-1) TOPIC : SIMPLE HARMONIC MOTION AND WAVES (PHYSICS) Duration : 1 Hour Max. Marks : 90 GENERAL INSTRUCTIONS 1. This Question Paper contains 30 objective type questions. 2. Each question has 4 choices (A), (B), (C) and (D), out of which only one is correct. 3. For each question, you will be awarded 3 Marks if you give the correct answer and zero Mark if no answer is given. In all other cases, minus one (–1) Mark will be awarded. Straight Objective Type This section contains 30 Single choice questions. Each question has choices (A), (B), (C) and (D), out of which ONLY ONE is correct. 1. The time taken by a particle performing SHM on a straight line to pass from point A to B where its velocities are same is 2 seconds. After another 2 seconds it returns to B. The time period of oscillation is (in seconds): (A) 2 (B) 4 (C) 6 (D) 8 2. For a particle in S.H.M., if the amplitude of displacement is ‘a’ and the amplitude of velocity is ‘v’ the amplitude of acceleration is : v2 (A) va (B) a v2 (C) 2a v (D) a 3. A body performs SHM along the straight line segment ABCDE with C as the mid point of segment AE (A and E are the extreme position for the SHM). Its kinetic energies at B and D are each one fourth of its maximum value. If length of segment AE is 2R, then the distance between B and D is : (A) 3 2 R (B) 4. A system is shown in the figure. The time period for small oscillations of the two blocks will be : (A) 2  (B) 2  (C) 2  (D) 2  5. Two light strings, each of length 𝑙, are fixed at points A and B on a fixed horizontal rod xy. A small bob is tied by both strings and in equilibrium, the strings are making angle 45° with the rod. If the bob is sl ightly displaced normal to the plane of the strings and released then period of the resulting small oscillation will be : (A) 2 (B) 2 (C) 2 (D) 2 6. A metre stick swinging in vertical plane about a fixed horizontal axis passing through its one end undergoes small oscillation of frequency f0 as shown in figure. If the bottom half of the stick were cut off, then its new frequency of small oscillation would become: (A) f0 (B) f0 (C) 2f0 (D) 2 f0 7. A 25 kg uniform solid sphere with a 20 cm radius is suspended by a vertical wire such that the point of suspension is vertically above the centre of the sphere. A torque of 0.10 N-m is required to rotate the sphere through an angle of 1.0 rad and then maintain the orientation. If the sphere is then released, its time period of the oscillation will be : (A)  second (B) 2  second (C) 2 second (D) 4 second 8. A rod of length 𝑙 is in motion such that its ends A and B are moving d along x-axis and y-axis respectively. It is given that dt = 2 rad/s always. P is a fixed point on the rod as shown in figure. Let M be the projection  of P on x-axis. For the time interval in which  changes from 0 to 2 , choose the correct statement : (A) The acceleration of M is always directed towards right (B) M executes SHM (C) M moves with constant speed (D) M moves with constant acceleration 9. Which of the following is greatest in SHM ? (assuming potential energy = 0 at mean position) (A) Average kinetic energy with respect to position (B) Average potential energy with respect to position (C) Average kinetic energy with respect to time (D) Average potential energy with respect to time 10. m1 & m2 are connected with a light inextensible string with m1 lying on smooth table and m2 hanging as shown in figure. m1 is also connected to a light spring which is initially unstretched and the system is released from rest : (A) system performs SHM with angular frequency given by k(m1m2 ) m1m2 (B) system performs SHM with angular frequency given by . (C) tension in string will be zero when the system is released. (D) maximum displacement of m1 will be m2 g . k 11. The potential energy of a particle executing SHM changes from maximum to minimum in 5 sec. Then the time period of SHM is : (A) 5 s (B) 10 s (C) 15 s (D) 20 s 12. A body is executing simple harmonic motion. At a displacement x from mean position, its potential energy is E1 and at a displacement y from mean position, its potential energy is E2. The potential energy E at a displacement (x + y) from mean position is (the potential energy is zero at mean position) : (A) E1 + E2 (B) (C) E1 + E2 + 2 (D) 13. In the figure shown a block of mass m is attached at ends of two springs. The other ends of the spring are fixed. The mass m is released in the vertical plane when the spring are relaxed. The velocity of the block is maximum when: (A) k1 is compressed and k2 is elongated (B) k1 is elongated and k2 is compressed (C) k1 and k2 both are compressed (D) k1 and k2 both are elongated. 14. Figure shows the kinetic energy K of a simple pendulum versus its angle  from the vertical. The pendulum bob has mass 0.2 kg. The length of the pendulum is equal to (g = 10 m/s2) : (A) 2.0 m (B) 1.8 m (C) 1.5 m (D) 1.2 m 15. The equation of a wave is given by (all quantity expressed in S.I. units) Y = 5 sin10 (t – 0.01x) along the x-axis. The magnitude of phase difference between the points separated by a distance of 10 m along x- axis is : (A) /2 (B)  (C) 2 (D) /4. 16. A certain transverse sinusoidal wave of wavelength 20 cm is moving in the positive x direction. The transverse velocity of the particle at x = 0 as a function of time is shown. The amplitude of the motion is: 5  10 (A)  cm (B) 2 cm (C)  cm (D) 2 cm 17. Two vibrating strings of same material stretched under same tension and vibrating with same frequency in the same overtone have radii 2r and r. Then the ratio of their lengths is : (A) 1 : 2 (B) 1 : 4 (C) 1 : 3 (D) 2 : 3 18. A chord attached about an end to a vibrating fork divides it into 6 loops, when its tension is 36 N. The tension at which it will vibrate in 4 loops is: (A) 24 N (B) 36 N (C) 64 N (D) 81 N 19. Sinusoidal waves 5.00 cm in amplitude are to be transmitted along a string having a linear mass density equal to 4.00 × 10–2 kg/m. If the source can deliver a maximum power of 90 W and the string is under a tension of 100 N, then the highest frequency at which the source can operate is (take 2 = 10) : (A) 45.3 Hz (B) 50 Hz (C) 30 Hz (D) 62.3 Hz 20. What is the percentage change in the tension necessary in a sonometer of fixed length to produce a note one octave lower (half of original frequency) than before : (A) 25% (B) 50% (C) 67% (D)75% 21. Figure shown is a graph, at a certain time t, of the displacement function S(x,t) of three sound waves 1,2 and 3 as marked on the curves that travel along x–axis through air. If P1,P2 and P3 represent their pressure amplitudes respectively, then correct relation between them is : (A) P1 > P2 > P3 (B) P3 > P2 > P1 (C) P1 = P2 = P3 (D) P2 > P3 > P1 22. Under similar conditions of temperature and pressure, In which of the following gases the velocity of sound will be largest : (A) H2 (B) N2 (C) He (D) CO2 23. In a sound wave, to increase the intensity by a factor of 10, pressure amplitude must be changed by a factor of : (A) (B) 10 (C) 10 (D) 24. The two pipes are submerged in sea water, arranged as shown in figure. Pipe A with length LA = 1.5 m and one open end, contains a small sound source that sets up the standing wave with the second lowest resonant frequency of that pipe. Sound from pipe A sets up resonance in pipe B, which has both ends open. The resonance is at the second lowest resonant frequency of pipe B. The length of the pipe B is : (A) 1 m (B) 1.5 m (C) 2 m (D) 3 m 25. A source of sound of frequency 256 Hz is moving rapidly towards a wall with a velocity of 5 m/sec. If sound travels at a speed of 330 m/sec, then number of beats per second heard by an observer between the wall and the source is: (A) 7.7 Hz (B) 9 Hz (C) 4 Hz (D) none of these 26. 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: (A) 1 m/s (B) 2 m/s (C) 0.5 m/s (D) 1.5 m/s 27. A source of frequency f is stationary and an observer starts moving towards it at t = 0 with constant small acceleration. Then the variation of observed frequency f ' registered by the observer with time is best represented as : (A) (B) (C) (D) 28. Two persons A and B each carrying a source of frequency 596 Hz and 600 Hz respectively are standing at rest a few metres apart. A starts A B moving towards B with a velocity of 2 m/s. If the speed of sound is 300 m/s. Which of the following statement is true? (A) Beats heard per second by A is zero and B is 8. (B) Beats heard per second by A is 8 and B is zero. (C) Frequency of B heard by A is 600 Hz. (D) Frequency of A as heard by B is 604 Hz. 29. In a horizontal spring–mass system, mass m is released after being displaced towards right by some distance at t = 0 on a frictionless surface. The phase angle of the motion in radian when it is first time passing through the equilibrium position is equal to : (A) /2 (B)  (C) 3/2 (D) 0 30. A 75 cm string fixed at both ends produces resonant frequencies 384 Hz and 288 Hz without there being any other resonant frequency between these two. Wave speed for the string is : (A) 144 m/s (B) 216 m/s (C) 108 m/s (D) 72 m/s A nswers 1. (D) 2. (B) 3. (C) 4. (C) 5. (D) 6. (B) 7. (D) 8. (B) 9. (A) 10. (B) 11. (D) 12. (C) 13. (B) 14. (C) 15. (B) 16. (C) 17. (A) 18. (D) 19. (C) 20. (D) 21. (B) 22. (A) 23. (A) 24. (C) 25. (D) 26. (C) 27. (A) 28. (B) 29. (B) 30. (A) PART TEST - 2 (PT-2) TOPIC : SIMPLE HARMONIC MOTION AND WAVES (PHYSICS) Duration : 1 Hour Max. Marks : 88 GENERAL INSTRUCTIONS 1. This Question Paper contains 24 questions. 2. For each question in Section I , you will be awarded 3 Marks if you give the correct answer and zero Mark if no answer is given. In all other cases, minus one (–1) Mark will be awarded. 3. For each question in Section II , you will be awarded 4 Marks if you give the correct answer. There is no negative marking. 4. For each question in Section III, you will be awarded 3 Marks if you give the correct answer and zero Mark if no answer is given. In all other cases, minus one (–1) Mark will be awarded. 5. For each question in Section IV, you will be awarded 4 Marks if you give the correct answer and zero Mark if no answer is given. In all other cases, minus one (–1) Mark will be awarded. 6. For each question in Section V, you will be awarded 6 Marks if you give ALL the correct answer(s) or awarded : (i) 1 Mark for correct answer in one row. (ii) 2 Marks for correct answer in two rows. (iii) 4 Marks for correct answer in three rows. SECTION - I Straight Objective Type This section contains 8 Single choice questions. Each question has choices (A), (B), (C) and (D), out of which ONLY ONE is correct. 1. A particle performs SHM with a time period T and amplitude 'a'. The magnitude of average velocity of the particle over the time interval during which it travels a distance a from the extreme position is : 2 (A) a (B) 2a T T (C) 3a T (D) 2T 2. A simple pendulum 50 cm long is suspended from the roof of a cart accelerating in the horizontal direction with constant acceleration g m/s2. The period of small oscillations of the pendulum about its equilibrium position is (g = 2 m/s2) : (A) 1.0 sec (B) sec (C) 1.53 sec (D) 1.68 sec 3. A particle is subjected to two simple harmonic motions along x and y directions according to, x = 3 sin 100  t; y = 4 sin 100  t : (A) Motion of particle will be on ellipse traversing it in clockwise direction. (B) Motion of particle will be on a straight line with slope 4/3. (C) Motion will be a simple harmonic motion along x - axis with amplitude 5. (D) Phase difference between two motions is /2. 4. When a wave pulse traveling in a string is reflected from a rigid wall to which string is tied as shown in figure. For this situation two statements are given below : (1) The reflected pulse will be in same orientation of incident pulse due to a phase change of  radians (2) During reflection the wall exert a force on string in upward direction For the above given two statements choose the correct option given below : (A) Only (1) is true (B) Only (2) is true (C) Both are true (D) Both are wrong 5. The equation of displacement due to a sound wave is s = s sin2 (t  k x). If the bulk modulus of the medium is B, then the equation of pressure variation due to that sound is : (A) B k s0 (C) B k s0 sin (2  t  2 k x) (B)  B k s cos2 ( t  k x) (D)  B k s sin (2  t  2 k x) cos2 ( t  k x) 6. A point source of power 50 watts is producing sound waves of frequency 1875Hz. The velocity of sound is 330m/s, atmospheric pressure is 1.0 x 105 Nm2, density of air is 1.0 kgm3. Then pressure amplitude at r = m from the point source is (using  = 22/7) : (A) 5 Nm-2. (B) 10 Nm-2. (C) 15 Nm-2. (D) 20 Nm-2. 7. An organ pipe of length L is open at one end and closed at other end. The wavelengths of the three lowest resonating frequencies that can be produced by this pipe are : (A) 4L, 2L, L (B) 2L, L, L/2 (C) 2L, L, 2L/3 (D) 4L, 4L/3, 4L/5 8. A wire having a linear mass density 5.0  10 3 kg/m is stretched between two rigid supports with a tension of 450 N. The wire resonates at a frequency of 420 Hz. The next higher frequency at which the same wire resonates is 480 Hz. The length of the wire is : (A) 2.0 m (B) 2.1 m (C) 2.5 m (D) 3 m SECTION - II Multiple Correct Answers Type This section contains 4 Multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONE OR MORE may be correct. 9. A particle is executing SHM between points -Xm and Xm, as shown in figure-I. The velocity V(t) of the particle is partially graphed and shown in figure-II. Two points A and B corresponding to time t1 and time t2 respectively are marked on the V(t) curve : V +x (A) At time t1 , it is going towards Xm. (B) At time t1, its speed is decreasing. (C) At time t2, its position lies in between –Xm and O. (D) The phase difference  between points A and B must be expressed as 90° <  < 180°. 10. In a standing wave on a string rigidly fixed at both ends. (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 one time period. (D) All the particles are never at rest simultaneously. 11. For a certain transverse standing wave on a long string, an antinode is formed at x = 0 and next to it, a node is formed at x = 0.10 m. the displacement y(t) of the string particle at x = 0 is shown in figure. 4 y(cm) t(s) -4 (A) Transv erse displacement of the particle at x = 0.05m and t = 0.05 s is – 2 (B) Transverse displacement of the particle at x = 0.04 m and t = 0.025 s is – 2 cm. cm. (C) Speed of the traveling waves that interfere to produce this standing wave is 2 m/s. 1 (D) The transverse velocity of the string particle at x = 15 m and t = 0.1 s is 20  cm/s 12. A wave pulse moving in the positive x-direction along the x-axis is represented by the wave function y (x, t) = 2.0 (x  3.0 t)2  1 , where x and y are in centimeters and t is in seconds. Then (A) The speed of particle at time t = 1 sec. and x = 3cm is zero. (B) The speed of particle at time t = 1 sec. and x = 3cm is 2 cm/s. (C) The speed of the pulse is 3.0 cm/s (D) The speed of the pulse is 0.33 cm/s SECTION - III Reasoning Type This section contains 4 Reasoning type questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. 13. Statement-1 : A particle is moving along x-axis. The resultant force F acting on it is given by F = – ax – b. Where a and b are both positive constants. The motion of this particle is not SHM. Statement-2 : In SHM resultant force must be proportional to the displacement from mean position. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True 14. Statement-1 : Two waves moving in a uniform string having uniform tension cannot have different velocities. Statement-2 : Elastic and inertial properties of string are same for all waves in same string. Moreover speed of wave in a string depends on its elastic and inertial properties only. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True 15. Statement-1 : In a small segment of string carrying sinusoidal wave, total energy is conserved. Statement-2 : Every small part moves in SHM and in SHM total energy is conserved. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True 16. Statement-1 : When two vibrating tuning forks having frequencies 256 Hz and 512 Hz are held near each other, beats cannot be heard. Statement-2 : The principle of superposition of waves is valid only if the frequencies of both the interfering waves are equal or nearly equal. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True. SECTION - IV Comprehension Type This section contains 2 Paragraphs. Based upon each paragraph, 3 Multiple choice questions have to be answered. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. Comprehension (For Q.No. 17 to 19) A small block of mass m is fixed at upper end of a massless vertical spring of spring constant K = 4mg and natural length '10L'. The lower end of spring is free L and is at a height L from fixed horizontal floor as shown. The spring is initially unstressed and the spring-block system is released from rest in the shown position. 17. At the instant speed of block is maximum, the magnitude of force exerted by spring on the block is : (A) mg (B) mg 2 (C) Zero (D) None of these 18. As the block is coming down, the maximum speed attained by the block is : (A) (B) (C) (D) 19. Till the block reaches its lowest position for the first time, the time duration for which the spring remains compressed is : (A)  + 1 sin–1 3 (B) (B) 1 + sin–1 3 (C)  + 2 sin–1 3 (D) (D) 2 + sin–1 3 Comprehension (For Q.No. 20 to 22) There is a point source of sound placed at (0, h) as shown in figure. Two detectors D1 and D2 are placed at positions (D,d/2) and (D,– d/2) respectively. Take h < < D. The source emitted a sound pulse at a certain time. Assuming velocity of sound in the surrounding medium is v. (0, 20. The time gap between the recordings made by the detectors will approximately be : (A) 1 d h 2 Dv d h (B) 2 D v (C) hd (D) None of these Dv 21. If the source emits continuous waves, and the pressures recorded by the two detectors are superposed at every instant in detector D0 (which is equidistant from D1 & D2), the resultant pressure amplitude will be maximum if the minimum frequency of the source is : (A) 1 2 vD d.h vD (B) 2 d.h (C) 3 2 vD d.h (D) (D) vD d.h 22. If the source is shifted slightly towards positive X direction. The minimum frequency required for the super posed pressure amplitude (detected at D0) to be maximum will (as compared to the answer in above question) : (A) Decrease (B) Increase (C) Remain same (D) Nothing can be said SECTION - IV Matrix - Match Type This section contains 2 questions. Each question has four statements (A, B, C and D) given in Column-I and four or five statements (p,q,r, s or p,q,r, s,t) in Column-II. Any given statement in Column-I can have correct matching with ONE OR MORE statement(s) in Column-II. The answers to these questions have to be appropriately marked as illustrated in the following example. If the correct matches are A-p, A-r, B-p, B-s, C-r, C-s, D-q and D-t then the answer should be written as : A  p,r ; B p, s ; C  r, s ; D  q, t. 23. In the column-I, a system is described in each option and corresponding time period is given in the column-II. Suitably match them. Column-I Column-II (A) A simple pendulum of length '𝑙' oscillating (p) T = 2 with small amplitude in a lift moving down with retardation g/2. (B) A block attached to an end of a vertical (q) T = 2 spring, whose other end is fixed to the ceiling of a lift, stretches the spring by length '𝑙' in equilibrium. It's time period when lift moves up with an acceleration g/2 is (C) The time period of small oscillation of a (r) T = 2 uniform rod of length '𝑙' smoothly hinged at one end. The rod oscillates in vertical plane. (D) A cubical block of edge '𝑙' and specific (s) T = 2 density /2 is in equilibrium with some volume inside water filled in a large fixed container. Neglect viscous forces and surface tension. The time period of small oscillations of the block in vertical direction is 24. Match the statements in column- with the statements in column-. Column-I Column-II (A) A tight string is fixed at both ends and (p) At the middle, antinode is formed sustaining standing wave in odd harmonic (B) A tight string is fixed at one end and (q) At the middle, node is formed free at the other end in even harmonic (C) Standing wave is formed in an open organ (r) At the middle, neither node nor pipe. End correction is not negligible. antinode is formed (D) Standing wave is formed in a closed (s) Phase difference between SHMs of any organ pipe. End correction is not negligible. two particles will be either  or zero. (t) The displacement of the particle in the middle is always non zero. A nswers 1. (C) 2. (A) 3. (B) 4. (D) 5. (A) 6. (A) 7. (D) 8. (C) 9. (B)(C) 10. (A)(C) 11. (A)(C)(D) 12. (A)(C) 13. (D) 14. (D) 15. (D) 16. (C) 17. (B) 18. (C) 19. (B) 20. (C) 21. (D) 22. (A) 23. (A) p (B) q (C) p (D) s 24. (A) p,q,s (B) r,s (C) s (D) r,s PART TEST - 3 (PT-3) TOPIC : SIMPLE HARMONIC MOTION AND WAVES (PHYSICS) Duration : 1 Hour Max. Marks : 88 GENERAL INSTRUCTIONS 1. This Question Paper contains 22 questions. 2. For each question in Section I, you will be awarded 3 Marks if you give the correct answer and zero Mark if no answer is given. In all other cases, minus one (–1) Mark will be awarded. 3. For each question in Section II, you will be awarded 4 Marks if you give the correct answer. There is no negative marking. 4. For each question in Section III, you will be awarded 3 Marks if you give the correct answer and zero Mark if no answer is given. In all other cases, minus one (–1) Mark will be awarded. 5. For each question in Section IV, you will be awarded 4 Marks if you give the correct answer and zero Mark if no answer is given. In all other cases, minus one (–1) Mark will be awarded. 6. For each question in Section V, you will be awarded 6 Marks if you give ALL the correct answer(s) or awarded : (i) 1 Mark for correct answer in one row. (ii) 2 Marks for correct answer in two rows. (iii) 4 Marks for correct answer in three rows. 7. For each question in Section VI, you will be awarded 6 Marks if you give the correct answer. There is no negative marking. SECTION - I Straight Objective Type This section contains 8 Single choice questions. Each question has choices (A), (B), (C) and (D), out of which ONLY ONE is correct. 1. A particle undergoes SHM with a time period of 2 seconds. In how much time will it travel from its mean position to a displacement equal to half of its amplitude : (A) 1/2 sec (B) 1/3 sec (C) 1/4 sec (D) 1/6 sec. 2. A horizontal rod of mass m and length L is pivoted smoothly at one end. The rod ’s other end is supported by a spring of force constant k. The rod is rotated (in vertical plane) by a small angle  from its horizontal equilibrium position and released. The angular f requency of the subsequent simple harmonic motion is : (A) (B) (C) (D) 3. A traveling wave y = A sin (k x –  t + ) passes from a heavier string to a lighter string. The reflected wave has amplitude 0.5 A. The junction of the strings is at x = 0. The equation of the reflected wave is: (A) y  = 0.5 A sin (k x +  t + ) (B) y  =  0.5 A sin (k x + t + ) (C) y  =  0.5 A sin ( t  k x  ) (D) y  = – 0.5 A sin (k x +  t  ) 4. A string of length 1.5 m with its two ends clamped is vibrating in fundamental mode. Amplitude at the centre of the string is 4 mm. Minimum distance between the two points having amplitude 2 mm is: (A) 1 m (B) 75 cm (C) 60 cm (D) 50 cm 5. The average density of Earth’s crust 10 km beneath the surface is 2.7 gm/cm3. The speed of longitudnal seismic waves at that depth is 5.4 km/s. The bulk modulus of Earth’s crust considering its behavior as fluid at that depth, is : (A) 7.9 × 1010 Pa (B) 5.6 × 1010 Pa (C) 7.9 × 107 Pa (D) 1.46 × 107 Pa 6. The second overtone of an open pipe A and a closed pipe B have the same frequencies at a given temperature. Both pipes contain air. The ratio of fundamental frequency of A to the fundamental fre- quency of B is: (A) 3: 5 (B) 5: 3 (C) 5: 6 (D) 6: 5 7. A thin uniform rod is suspended in vertical plane as a physical pendulum about point A A. The time period of oscillation is To. Not counting the point A, the number 'n' of other points of suspension on rod such that the time period of oscillation (in vertical plane) is again To. Then the value of n is : (Since the rod is thin, consider one point for each transverse cross section of rod) (A) 0 (B) 1 (C) 2 (D) 3 B 8. Two radio station that are 250m apart emit radio waves of wavelength 100m. Point A is 400m from both station. Point B is 450m from both station. Point C is 400m from one station and 450 m from the other. The radio station emit radio waves in phase. Which of the following statement is true ? (A) There will constructive interference at A and B, and destructive interference at C. (B) There will be destructive interference at A and B, and constructive interference at C. (C) There will be constructive interference at B and C, and destructive interference at A. (D) There will be destructive interference at A, B and C. SECTION - II Multiple Correct Answers Type This section contains 4 Multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONE OR MORE may be correct. 9. A 20 gm particle is subjected to two simple harmonic motions : x1 = 2 sin 10 t,  x2 = 4 sin (10 t + 3 ). where x1 & x2 are in metre & t is in sec. (A) The displacement of the particle at t = 0 will be 2 m. (B) Maximum speed of the particle will be 20 m/s. (C) Magnitude of maximum acceleration of the particle will be 200 (D) Energy of the resultant motion will be 28 J. m/s2. 10. Which of the following wave(s) can produce standing wave when superposed with y = Asin (t + kx)? (A) Asin (t - kx + 300) (B) Acos (t - kx) (C) Asin (kx - t) (D) none of these 11. A spring block system is put into SHM in two experiments. In the first, the block is pulled from the equilibrium position through a displacement d1 and then released. In the second, it is pulled from the equilibrium position through a greater distance d2 and then released. In both the experiments: (A) Time period is same in both SHM. (B) frequency is same in both SHM (C) maximum kinetic energy is same in both SHM (D) angular frequency is same in both SHM 12 In Resonance tube experiment, if 400 Hz tuning fork is used, the first resonance occurs when length of air column is 19 cm. If the 400 Hz tuning fork is replaced by 1600 Hz tuning fork then to get resonance, the water level in the tube should be further lowered by (take end correction = 1 cm) : (A) 5 cm (B) 10 cm (C) 15 cm (D) 20 cm SECTION - III Reasoning Type This section contains 2 Reasoning type questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. 13. Statement-1 : A SHM may be assumed as composition of many SHM's. Statement-2 : Superposition of many SHM's (along same line) of same frequency will be a SHM. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True 14. Statement-1 : When a wave enters from one medium to another, its frequency is not changed. Statement-2 : Speed of a wave in a medium is property of the source. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True SECTION - IV Comprehension Type This section contains 1 Paragraphs. Based upon each paragraph, 3 Multiple choice questions have to be answered. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct. Comprehension (For Q. no. 15 to 17) A sinusoidal wave is propagating in negative x–direction in a string stretched along x-axis. A particle of string at x = 2m is found at its mean position and it is moving in positive y direction at t = 1 sec. The amplitude of the wave, the wavelength and the angular frequency of the wave are 0.1meter, /4 meter and 4 rad/sec respectively. 15. The equation of the wave is : (A) y = 0.1 sin [4t –1)+ 8(x – 2)] (B) y = 0.1 sin [t–1)– (x – 2)] (C) y = 0.1 sin [4t –1)–8(x – 2)] (D) none of these 16. The speed of particle at x = 2 m and t = 1sec is : (A) 0.2 m/s (B) 0.6 m/s (C) 0.4 m/s (D) 0 17. The instantaneous power transfer through x=2 m and t= 1.125 sec is : 4 (A) 10 J/s (B) 3 2 J/s (C) 3 J/s (D) 0 SECTION - V Matrix - Match Type This section contains 1 questions. Each question has four statements (A, B, C and D) given in Column-I and five statements (p,q,r, s and t) in Column-II. Any given statement in Column-I can have correct matching with ONE OR MORE statement(s) in Column-II. The answers to these questions have to be appropriately marked as illustrated in the following example. If the correct matches are A-p, A-r, B-p, B-s, C-r, C-s, D-q and D-t then the answer should be written as : A  p,r ; B p, s ; C  r, s ; D  q, t. 18. For a particle executing SHM along a straight line, match the statements in column-I with statement in column-II. (Note that displacement given in column- is to be measured from mean position). Column-I Column-II (A) Velocity-displacement graph may be (p) straight line (B) Acceleration-velocity graph may be (q) circle (C) Acceleration-displacement graph will be (r) ellipse (D) Acceleration-time graph will be (s) sine curve (t) cosine curve SECTION - VI Integer value correct Type This section contains 4 questions. The answer to each question is a integer type. 19. Two particles P1 and P2 are performing SHM along the same line about the same mean position. Initially they are at their positive extreme position. If the time period of each particle is 12 sec and the difference of their amplitudes is 12 cm then find the minimum time in seconds after which the separation between the particles become 6 cm. 20. A weightless rigid rod with a small iron bob at the end is hinged at point A to the wall so that it can rotate in all directions. The rod is kept in the horizontal position by a vertical inextensible string of length 20 cm, fixed at its mid point. The bob is displaced slightly, perpendicular to the plane of the rod and string. Find period of small oscillations of the system in the form X second. and fill value of X. (g = 10 m/s2) 10 21. A straight line source of sound of length L = 10m, emitts a pulse of sound that travels radially outward from the source. What sound energy (in mW) is intercepted by an acoustic cylindrical detector of surface area 2.4cm2, located at a perpendicular distance 7m from the source. The waves reach perpendicularly at the surface of the detector. The total power emitted by the source in the form of sound is 2.2 × 104 W. (Use  = 22/7) 22. In the figure shown strings AB and BC have masses m and 2m respectively. Both are of same length 𝑙. 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, 𝑙 = 9610 m, g = 10 m/s2, 1681 = 1.4, = 1.7 Then find the value of 't' in seconds . A nswers 1. (D) 2. (A) 3. (D) 4. (A) 5. (A) 6. (B) 7. (D) 8. (A) 9. (A)(B)(C)(D) 10. (A)(B)(C) 11. (A)(B)(D) 12 (A)(C) 13. (A) 14. (C) 15. (A) 16. (C) 17. (D) 18. (A) q,r (B) q,r (C) p (D) s, t 19. 2 20. 4 21. 12 22. 2