Physics Questions

The displacement x as a function of time t of a simple harmonic motion is represented by where A is a positive by constant 4 first increases and then decreases yo RPMT 2011 m a x dt A x 0 dx 2 A x 0 dt A x 0 dt d x The displacement y of a particle varies with time t in second as X cos 7 6 The time period of the dt A x 0

In forced oscillation of a particle the amplitude is maximum for a frequency of the force while the energy is maximum for a frequency oo of the force then Cit is a suenance AIEEE 2004 Condition 0 0 2 w 3 0 when damping is small and o when damping is large 4 c

Two simple harmonic motions are represented by the equations Y 0 1 sin 100nt y2 0 1 cos 100nt The phase difference of the velocity of particle 1 with respect to the velocity of particle 2 is A B C C w k 6 k 3 75 6 My Answer Correct Answer

A mass of 2 0 kg is put on a flat pan attached to a vertical spring fixed on the ground as shown in the figure The mass of the spring and the pan is negligible When pressed slightly and released the mass executes a simple harmonic motion The spring constant is 200N m What should be the minimum amplitude of the motion so that the mass gets AIPMT 2007 detached from the pan Take g 10 m s elllll m

3 between 0 and v 4 between U and The magnitude of average acceleration in half time period from equilibrium position in a simple harmonic motion is 1 2Am TC max 2 2 Aw 21 Aw 2T max 1952 4 Zero 3 tadionlacement y its potential energy is E and at a displacement y

AIPMT 2009 Which one of the following equation of motion represents simple harmonic motion 1 Acceleration kx k x 2 Acceleration k x a 4 Acceleration kx 3 Acceleration k x a The displacement of a particle along the x axis is given by x asin ot The motion of the particle corresponds to

A body is executing simple harmonic motion At a displacement x its potential energy is E and at a displacement y it potential energy is E The potential energy E at a displacement x y is 1 E E 2 E E 3 E E 2 E E 4 E E

3 y t 4 sin nt 2 y projection of the raidus vecotr of rotating particle P is 1 y t 3 cos It 2 5 where y in m P t 0 where y in m 3m T 4s X 2 y t 3 cos 2nt where y in m 4 y t 3 cos 3 t 2 where y in m NEET 20

3 I sec 4 0 5 sec A particle is oscillating freely with a natural frequency w and amplitude a It is later subjected damping force proportional to its velocity and keeps oscillating with a frequency oo Which of the follow statement is true RPMT 20 1 and the amplitude is not affected 3 and the amplitude remains the same 2 w w and the amplitude decreases with time 4 0 and the amplitude keep decreasing with time

The displacement of an object attached to a spring and executing simple harmonic motion is given by X 2 10 Cos t metres The time at which the maximum speed first occurs is AIEEE 2007 1 0 5 s 2 0 75 s 3 0 125 s 4 0 25 s the law y Y cos mt T 4 If the acceleration of the particle is

6 e The average energy in one time period in simple harmonic motion is C 1 m A 2 m w A 3 m A 4 4 zero harmonic motion with a frequency y The frequency with wh

A conducting sphere of radius 10 cm has an unknown charge The electric field at 30 cm from the surface of shell is 3 6 10 N C and points radially outwards What is total charge on the sphere O 16 nc O 32 nC O 64 NC O 42 nC 5

A particle of mass m is executing oscillations about the origin on the x axis Its potential energy is U x k x whe k is a positive constant If the amplitude of oscillation is a then its time period T is AIIMS 2008 1 proportional to 1 2 independent of a 3 proportional to a 4 proportional to a 2

Two particle are oscillating along two close parallel straight lines side by side with the same frequency and ampli tudes They pass each other moving in opposite directions when their displacement is half of the amplitude The mean positions of the two particles lie on a straight line perpendicular to the paths of the two particles The phase AIPMT 2011 difference is 1 0 2 2 3 3 T 4 6

21 Two pendulums at rest start swinging together Their lengths are respectively 1 44 m and 1 m They will again start swinging in same phase together after of longer pendulum 1 1 vibration 3 4 vibrations 4 5 vibrations imple nendulum as T in a lift at rest If the lift moves up with acceleration as 2 3 vibrations

A toy car of mass m is having two similar rubber ribbons attached to it as shown in the figure The force constant of each rubber ribbon is k and surface is frictionless The car is displaced from mean position by x cm and released At the mean position the ribbons are undeformed Vibration period is m 2k 1 2 2 2 m 2k k 3 2T k 4 2T m k k

A girl running on ground observes rain to be falling at a speed 10 m s The rain is falling vertically downward at a speed 6 m s with respect to girl when she was at rest The speed of the girl is 1 4 m s low 28 m s 3 2 m s 4 1 m s

20 Equipotential surfaces are shown in the region in x plane Electric field intensity in the region is 1 50 2 50 3 50 4 50 m M 3 V 30 10 V 15 V 20 V 20 cm 40 cm 120 from ve x axis 60 from ve x axis 30 from ve x axis 150 from ve x axis X

1 Straight line 2 Circle 3 Ellipse 4 Figure of eight Two mutually perpendicular simple harmonic vibrations have same amplitude frequency and phase When superimpose the resultant form of vibration will be 1 A circle 2 An ellipse 3 A straight line 4 A parabola

3 4f A particle of mass m executes simple harmonic motion with amplitude a and frequency u The average kinetic energy during its motion from the position of equilibrium to the end is AIEEE 2007 ma v 3 4n ma u 1 2 ma v 4 2 ma u When the mass M passes through its

The oscillation of a body on a smooth horizontal surface is represented by the equation X A cos cot where X displacement at time t frequency of oscillation Which one of the following graph shows correctly the variation a with t 1 180 Tt 2 AIPMT 2014 H M H Tt 3 4

1 3 5 2 25 9 3 A body executes simple harmonic motion The potential energy P E the kinetic energy K E and total ener T E are measured as function of displacement x Which of the following statements is true K E is maximum when x 0 2 T E is zero when x 0 2 K E is maximum when x is maximum 0 4 P E is maximum when x IRA 2 V AZ

1 10 cm 2 20 cm 17 32 Two particles execute S H M of same amplitude and frequency along the same straight line from same mean position They cross one another without collision when going in opposite directions each time their displacement is half of their amplitude The phase difference between them is 1 0 2 120 3 180 4 135 in thon correct graph for acceleration a and corresponding linea 5 100 1 x 95

A block of mass m is resting on a piston which is moving vertically with a SHM of period 1 s The minimum amplitude of motion at which the block and piston separate is O 0 50 2 25 m A mg 4 0 15 m

4 time period and displacement At how many maximum points velocity of simple pendulum is same 1 1 2 2 3 4 4 6 The velocity of a particle in S H M at displacement y from mean position is a amplitude o a IN

A block of mass m initially at rest is sliding up in vertical direction against a rough vertical wall with the help of a force F whose magnitude is constant but direction is changing 8 Bot where t 71 The value of F so that the block comes to rest when 2 is time in sec At t 0 the force is in vertical upward direction and then as time passes its direction is getting along normal i e 0 0 74 2 is

1 Increases 2 Decreases The mass and diameter of a planet are twice those of earth The period of osillation of pendulum on this planet will be If it is second s pendulum on earth 2 2 2 sec 1 sec 3 2 sec 4 sec

The position vector of a particle from origin is given by F A cosat jsinot The motion of the particle is 1 simple harmonic Ob 3 on a circle 2 on a straight line 3 4 with constant acceleration atents and in successive order The time periods of

33 When an oscillator completes 100 oscillation its ampliutde reduced to of initial value What will be its amplitude 3 when it completes 200 oscillation 400 27 1 1 2 2 3 3 4

The time period of a particle in simple harmonic motion is equal to the time between consecutive appearance of th particle at a particular point in its motion This point is 1 the mean position gnols 2 an extreme position 3 between the mean position and the positive extreme an position and the negative extreme

70 A wall clock uses a vertical spring mass system to measure the time Each time the mass reaches an extreme position the clock advances by a second The clock gives correct time at the equator If the clock is taken to the poles it will 4 give correct time 1 run slow 2 run fast 3 stop working A pendulum clock keeping correct time is taken to high altitudes 1 it will keen correct time

1 0 A mass M is performing linear simple harmonic motion then correct graph for acceleration a and corresponding line velocity v is M 85

6 Three identical resistors R R R are as shown to a battery of constant e m f The power dissipated is P www R R 1 The least in R 2 Greatest in R 3 In the ratio 1 2 in resistance R and R respectively 4 The same in R and in the parallel combination

21 5 A spring of force constant k is cut into lengths of ratio 1 2 3 They are connected in series and the new for constant is k Then they are connected in parallel and force constant is k Then k k is 1 1 9 NEET 201 2 1 11 4 1 6 3 1 14 ufficiently high building and is moving freely to and fro like a simple harm

irst decreases and then increases A 25 kg uniform solid sphere with a 20 cm radius is suspended by a vertical wire such that the point of suspensic vertically ab ove the centre of the sphere A torque of 0 10 N m is required to rotate the sphere through an angl 1 0 rad and then maintain the orientation If the sphere is then released its time period of the oscillation will be 1 second 3 2 second 2 2 second 4 4 second 2 2 0r1 0

1 0 25 m 2 0 52 m 3 2 5 m A particle moves on the X axis according to the equation x x sin oot The motion is simple harnomic 1 with amplitude x 2 with amplitude 2x T 3 with time period 2 S of amplitude of 0 1m When the particle passes through th 4 with time period

A mass M is suspended from a light spring An addtional mass mass added displaces the spring further by a distance x Now the combined mass will be oscillate on the spring with period 2 T 2 M m x mg 2 2 4 T 2 M m mgx 1 2D 1 T 2 mg x M m m 3 T n 2 mg x M m

Which of the following statements is not true In the case of a simple pendulum for small Teme perio 1 Directly proportional for square root of the length of the pendulum 2 Inversely proportional to the square root of the acceleration due to gravity 3 Dependent on the mass size and material of the bob 4 Independent of the amplitude

For a metallic conductor if p is resistivity at T and po is resistivity at reference temperature To then resistivity p is given by a is temperatu coefficient of resistivity 0 NCERT Pg 10 1 PT Po 1 T To 2 PT Po 1 a T To 3 PT Po 1 To T 4 T P 1 a T T

9 For a compound pendulum the maximum time period is L 2k 2 2 3 Zero 4 Infinite g g ring of radius R is suspended from its circumference and is made to oscillate about a horizontal axi 0 Np 3NR 1 2

1 A 2 2A 1 2 al potom s The distance moved by a particle in simple harmonic motion in one time period is L A 2 2A 3 4A 4 zerc gimple harmonic motion is equal to the time between cc

A student says that he had applied a force F k x on a particle and the particle moved in simple harmonic motion He refuses to tell whether k is a constant or not Assume that he has worked only with positive x and no other force acted on the particle 1 As x increases k increases 3 As x increases k remains constant 2 As x increases k decreases 4 The motion cannot be simple harmonic in proportional to

A simple pendulum has some time period T What will be the percentage change in its time period if its amplitud decreased by 5 1 6 4 0 2 3 3 1 5

The radius of cross section of the conductor of length varies linearly from a to 2a If the resistivity of the conductor is p and a the resistance of the conductor will be 0 pl 2 a 2p 5na na pl 2a

A simple pendulum is set up in a trolley which moves to the right with an acceleration a on a horizontal plane Then th thread of the pendulum in the mean position makes an angle 0 with the vertical due to the hosendo force a 1 tan in the forward direction 3 tan in the backward direction 3 a in the backward direction 2 tan 4 tan 18 in the forward direction

For a particle executing simple harmonic motion the acceleration is proportional to 2 distance from the mean position displacement from the mean position 3 distance travelled since t 0 4 speed

32 Two bodies M and N of equal masses are suspended from two separate massless spring of force constants k and k respectively If the two bodies oscillate vertically such that their maximum velocities are equal the ratio of the amplitude M to to that of N is A W ALW AL 33 Ar k AL K AL 53 3 ki ditic

DU KX 2 2 U KX 3 U K The kinetic energy and potential energy of a particle executing simple harmonic motion will be equal when displacement amplitude a is 1 2 a 2 2 a 2 3a when the displacement is half of the

The displacement of a particle in simple harmonic motion in one time period is 1 A AS 2 2A 1 2 al otome 3 4A 4 zer The distance moved by a particle in simple harmonic motion in one time period is

6 The average acceleration in one time period in a simple harmonic motion is 1 A w 2 A w 2 3 A 00 2 4 zero