NCERT Solutions for class 11 Physics | Chapter 14 - Oscillations

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Questions
1 A particle is in linear simple harmonic motion between two points A and B, 10 cm apart. Taken the direction from A to B as the +ve direction and choose the correct statements.

Oscillations

A the sign of velocity, acceleration, and force on the particle when it is 3 cm away from A going towards B are positive
B the sign of velocity of the particle at C going towards O is negative
C the sign of velocity, acceleration, and force on the particle when it is 4 cm away from B going towards A are negative
D the sign of acceleration and force on the particle when it is at point B is negative

Answer:A, C, D
2 A body is performing SHM. Then its
A average total energy per cycle is equal to its maximum kinetic energy
B average kinetic energy per cycle is equal to half of its maximum kinetic energy
C mean velocity over a complete cycle is equal to 2/π times of its maximum velocity
D root mean square velocity is 1/√2 times of its maximum velocity

Answer:A, B, D
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3 The displacement time graph of a particle executing SHM is shown in the figure. Which of the following statement is/are true?

Oscillations

A the force is zero at t = 3T/4
B the acceleration is maximum at t = 4T/4
C the velocity is maximum at t = T/4
D the PE is equal to KE of oscillation t = T/2

Answer:A, B, C
4 Which of the following statements is/are true for a simple harmonic oscillator?
A force acting is directly proportional to the displacement from the mean position and opposite to it
B motion is periodic
C acceleration of the oscillator is constant
D the velocity is periodic

Answer:A, B, D
5 Displacement versus time curve for a particle executing SHM is shown in the figure. Choose the correct statements.

Oscillations

A phase of the oscillator is same at t = 0 s and t = 2 s
B phase of the oscillator is the same at t = 2 s and t = 6 s
C phase of the oscillator is the same at t = 1 s and t = 7 s
D phase of the oscillator is the same at t = 1 s and t = 5 s

Answer:B, D
6 The motion of a ball bearing inside a smooth curved bowl, when released from a point slightly above the lower point is
A simple harmonic motion
B non-periodic motion
C periodic motion
D periodic but not SHM

Answer:A, B
7 The rotation of the earth about its axis is
A periodic motion
B simple harmonic motion
C periodic but not simple harmonic motion
D non-periodic motion

Answer:A, C
8 A particle executing SHM has a maximum speed of 30 cm/s and a maximum acceleration of 60 cm/s2. The period of oscillation is
A πs
B π/2 s
C 2 πs
D π/t s

Answer:πs
9 The equation of motion of a particle is x = a cos (αt)2. The motion is
A periodic but not oscillatory
B periodic and oscillatory
C oscillatory but not periodic
D neither periodic nor oscillatory

Answer:oscillatory but not periodic
10 Figure shows the circular motion of a particle. The radius of the circle, the period, sense of revolution, and the initial position are indicated on the figure. The simple harmonic motion of the x-projection of the radius vector of the rotating particle P is

Oscillations

A x(t) = B sin (2πt/30)
B x(t) = B cos (πt/15)
C x(t) = B sin (πt/15 + π/2)
D x(t) = B cos (πt/15 + π/2)

Answer:x(t) = B sin (2πt/30)
11 Four pendulums A, B, C, and D are suspended from the same elastic support as shown in the figure. A and C are of the same length, while B is smaller than A and D is larger than A. If A is given a transverse displacement,

Oscillations

A D will vibrate with maximum amplitude
B C will vibrate with maximum amplitude
C B will vibrate with maximum amplitude
D all the four will oscillate with equal amplitude

Answer:C will vibrate with maximum amplitude
12 The displacement of a particle varies with time according to the relation y = a sin ωt + b cos ωt
A the motion is oscillatory but not SHM
B the motion is SHM with amplitude a + b
C the motion is SHM with amplitude a2 + b2
D the motion is SHM with amplitude √a2 + b2

Answer:the motion is SHM with amplitude √a2 + b2
13 A particle is acted simultaneously by mutually perpendicular simple harmonic motions x = a cos ωt and y = a sin ωt. The trajectory of motion of the particle will be
A an ellipse
B a parabola
C a circle
D a straight line

Answer:a circle
14 Motion of an oscillating liquid column in a U-tube is
A periodic but not simple harmonic
B non-periodic
C simple harmonic and time period is independent of the density of the liquid
D simple harmonic and time period is directly proportional to the density of the liquid

Answer:simple harmonic and time period is independent of the density of the liquid
15 The relation between acceleration and displacement of four particles are given below:
A ax = +2x
B ax = +2x2
C ax = -2x2
D ax = -2x

Answer:ax = -2x
16 The displacement of a particle is represented by the equation y = sin3 ωt. The motion is
A non-periodic
B periodic but not simple harmonic
C simple harmonic with period 2π/ω
D simple harmonic with period π/ω

Answer:simple harmonic with period 2π/ω
17 The displacement of a particle is represented by the equation y = 3 cos(π/4 – 2ωt). The motion of the particle is
A simple harmonic with period 2p/w
B simple harmonic with period π/ω
C periodic but not simple harmonic
D non-periodic

Answer:simple harmonic with period π/ω
18 Which of the following does not exhibit polarization
A Longitudinal wave in a gas
B Transverse wave in a gas
C Neither (a) nor (b)
D Both (a) and (b)

Answer:Longitudinal wave in a gas
19 he length of the pendulum which is displaying SHM is increased by 21%. Calculate the percentage increase in the periodic time of the pendulum.
A 21%
B 10%
C 11%
D 42%

Answer:10%
20 The observer hears a sound from the source which is moving away from the observer who is stationary. Determine the frequency of the sound
A It is halved
B It remains the same
C It reaches infinity
D It gets doubled

Answer:It is halved

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