OBJECTIVE QUESTIONS FOR NEET AIIMS JIPMER www.wisedane.com

PHYSICS OSCILLATION SET 1 MCQ’S www.wisedane.com

Q1. Two particles are executing S. H. M Q1. Two particles are executing S.H.M. of same amplitude and Frequency along the same straight line path. They pass each other when going in opposite direction, each time their displacement is half of their amplitude. What is the phase difference between them? www.wisedane.com

ANSWER (B) EXPLANATION www.wisedane.com

Q2. The displacement of two particles executing SHM are represented by equations 𝑦 1 =2 𝑠𝑖𝑛 10𝑡+𝜃 , 𝑦 2 =3 𝑐𝑜𝑠 10 𝑡. The phase difference between the velocity of these particles is: θ −θ θ+π/2 θ−π/2 www.wisedane.com

ANSWER (D) EXPLANATION www.wisedane.com

Q3. Two pendulums have time period T and 5 T/4. They start S. H. M Q3. Two pendulums have time period T and 5 T/4. They start S.H.M. at the same time from the mean position. What will be the phase difference between them after the bigger pendulum completed one oscillation ? 45o 90o 60o 30o www.wisedane.com

ANSWER (B) EXPLANATION When bigger pendulum of time period (5 T/4) completes one vibration, the smaller pendulum will complete (5/4) vibrations. It means the smaller pendulum, will be leading the bigger pendulum by phase T/4 sec = 𝜋 2 𝑟𝑎𝑑=90o. www.wisedane.com

Q4. A particle executes S. H. M Q4. A particle executes S.H.M. then the graph of velocity as a function of displacement is : A straight line A circle An ellipse A hyperbola www.wisedane.com

ANSWER (C) EXPLANATION www.wisedane.com

Q5. Acceleration (a) –displacement (x) graph of a particle executing SHM is as shown in figure. The time period of its oscillation is sec is : π 4 π 2 π 2π www.wisedane.com

ANSWER (D) EXPLANATION www.wisedane.com

Q6. A body of mass 5 gram is executing S. H. M. about a fixed point O Q6. A body of mass 5 gram is executing S.H.M. about a fixed point O. With an amplitude of 10 cm, its maximum velocity is 100 cm/s. Its velocity will be 50 cm 𝒔 −𝟏 𝒂𝒕 𝒂 distance (in cm) 5 5 2 5 3 10 2 www.wisedane.com

ANSWER (C) EXPLANATION www.wisedane.com

Q7. A coin is placed on a horizontal platform, which undergoes horizontal SHM about a mean position O. The coin placed on platform does not slip, when angular frequency of the SHM is 𝝎. The coefficient of friction between the coin and the platform is 𝝁. The amplitude of oscillation is gradually increased. The coil will begin to slip on the platform for the first time, At the mean position At the extreme position of oscillation For an amplitude of 𝜇 𝑔/ 𝜔 2 For an amplitude of 𝑔/𝜇 𝜔 2 www.wisedane.com

ANSWER (C) EXPLANATION Let O be the mean position and 𝑥 be the distance of coin from O. The coin will slip if centrifugal force on coin just becomes equal to force of friction, i.e., 𝑚𝑥 𝜔 2 =𝜇 𝑚𝑔 The coin will slip if 𝑥= maximum = amplitude A. www.wisedane.com

Q8. A horizontal plank has a rectangular block placed on it Q8. A horizontal plank has a rectangular block placed on it. The plank start oscillating vertically and simple harmonically with an amplitude of 40 cm. the block just loses contact with the plank when the later is momentary at rest. Then The period of oscillation is 2𝜋/5 𝑠𝑒𝑐 The block weighs double its weight when the plank is at one of the positions of momentary at rest The block weighs 1.5 times its weight on the plank half way down The block weighs its true weight on the plank when the latter moves fastest www.wisedane.com

ANSWER (B) EXPLANATION At one of the extreme position, wt of block = restoring force. At the other extreme position wt of block and restoring force both act downward directions. So the wt of block there is double than its weight. www.wisedane.com

Q9. Maximum speed of a particle in SHM is 𝒗 𝒎𝒂𝒙 Q9. Maximum speed of a particle in SHM is 𝒗 𝒎𝒂𝒙. Then average speed of a particle is SHM is equal to : www.wisedane.com

ANSWER (D) EXPLANATION Let r be the amplitude of oscillation and T be the time period in SHM. Then total distance travelled in time T = 4 r. www.wisedane.com

Q10. The bob of a simple pendulum of length L is released at time t = 0 from a position of small angular displacement. Its linear displacement at time t is given by : www.wisedane.com

ANSWER (D) EXPLANATION As the bob of simple pendulum released from the position of small angular displacement, hence when t = 0, the bob is at the extreme position. www.wisedane.com

Q11. The motion of a particle varies with time according to the relation 𝒚=𝒂 𝒔𝒊𝒏 𝝎𝒕+𝒃 𝒄𝒐𝒔 𝝎𝒕 The motion of oscillatory but not S.H.M. The motion is S.H.M. with amplitude a + b The motion is S.H.M. with amplitude a2+b2 The motion is S.H.M. with amplitude 𝑎 2 + 𝑏 2 www.wisedane.com

ANSWER (D) EXPLANATION www.wisedane.com

Q12. The composition of two simple harmonic motions of equal periods at right angle to each other and with a phase difference of 𝝅 results in the displacement of the particle along Circle Figure of eight Straight line Ellipse. www.wisedane.com

ANSWER (C) EXPLANATION www.wisedane.com

Q13. A mass m = 100 gms is attached at the end of light spring which oscillates on a frictionless horizontal table with an amplitude equal to 0.16 metres and time period equal to 2 sec. Initially the mass is released from rest at t = 0 and displacement 𝒙=−𝟎.𝟏𝟔 𝒎. The expression for the displacement of the mass at any time (t) is : x=0.16 cos (πt+x) x=−0.16 cos (πt+x) x=0.16 cos (πt) x=−0.16 cos (πt) www.wisedane.com

ANSWER (D) EXPLANATION www.wisedane.com

Q14. If a simple pendulum of length 𝒍 has maximum angular displacement 𝜽, then the maximum kinetic energy of bob of mass m is : www.wisedane.com

ANSWER (C) EXPLANATION www.wisedane.com

Q15. For a simple Harmonic Oscillator, the potential energy is equal to kinetic energy Once during each cycle Twice during each cycle when x=a/2 when x=a www.wisedane.com

ANSWER (B) EXPLANATION Total energy = P.E. + K.E. When a particle executes S.H.M., there will be two positions in each cycle where the P.E. is equal to K.E. of the body in S.H.M. www.wisedane.com

Q16. For a simple pendulum executing S.H.M. in air, the ratio of K.E. when it passes through the equilibrium position and its P.E. When it has maximum amplitude is : Less than one Greater than one Equal to one Equal to half www.wisedane.com

ANSWER (B) EXPLANATION K.E. at the mean position = work done against air friction and gravity. Therefore, K.E. = workdone against air resistance + P.E. So K.E./P.E. >1. www.wisedane.com

For what value of 𝜔 energy of both the particles is same ? Q17. The displacement of two identical particles executing SHM are represented by equations 𝑥 1 =8 𝑠𝑖𝑛 10 𝑡+ 𝜋 6 𝑎𝑛𝑑 𝑥 2 =5 𝑐𝑜𝑠 𝜔𝑡 𝑠𝑖𝑛 10 𝑡+ 𝜋 6 𝑎𝑛𝑑 𝑥 2 =5 𝑐𝑜𝑠 𝜔𝑡 For what value of 𝜔 energy of both the particles is same ? 4 units 8 units 16 units 20 units www.wisedane.com

ANSWER (C) EXPLANATION www.wisedane.com

Q18. When the displacement is half of the amplitude, then what fraction of the total energy of a simple harmonic oscillator is kinetic ? 2/7 th 3/4 th 2/9 th 5/7 th www.wisedane.com

ANSWER (B) EXPLANATION www.wisedane.com

Q19. A mass M is suspended from a spring of negligible mass Q19. A mass M is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes simple harmonic oscillation with a time period T. If the mass is increased by m, then the time period becomes 𝟓 𝟒 𝐓 . 𝐓𝐡𝐞 𝐫𝐚𝐭𝐢𝐨 𝐨𝐟 𝐦 𝐌 𝐢𝐬 9/16 5/4 25/16 4/5 www.wisedane.com

ANSWER (A) EXPLANATION www.wisedane.com

Q20. For a body of mass m attached to the spring, the spring factor is given by (𝝎, the angular frequency) www.wisedane.com

ANSWER (B) EXPLANATION www.wisedane.com