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Question (1)

QN0038556

The displacement of a particle is represented by the equation . The motion of the particle is

(A)
simple harmonic with period
(B)
simple harmonic with period
(C)
periodic but not simple harmonic
(D)
non-periodic

Correct Answer: B

Explanation:

As given that,

Velocity of the particle

So, acceleration,

In simple harmonic motion acceleration (or force) is directly proportional to the negative of displacement of particle as acceleration,

Hence, due to negative sign motion is simple harmonic motion (SHM.)

A simple harmonic motion is always periodic. So motion is periodic simple harmonic.

From the given equation,

Compare it by standard equation

So,

Hence, the motion is SHM with period .

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Question (2)

QN0038557

The displacement of a particle is represented by the equation . The motion is

(A)
non-periodic
(B)
periodic but not simple harmonic
(C)
simple harmonic with period
(D)
simple harmonic with period

Correct Answer: B

Explanation:

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Question (3)

QN0038558

The relation between acceleration and displacement of four particles are given below. Which, one of the particle is exempting simple harmonic motion?

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

Correct Answer: D

Explanation:

For motion to be SHM acceleration of the particle must be opposite of restoring force and proportional to negative of displacement. So, i.e., , so

Hence,

We should be clear that has to be linear.

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Question (4)

QN0038559

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

Correct Answer: C

Explanation:

Consider a U-tube filled in which a liquid column oscillates. When liquid column lifted upto height from to in arm . The liquid level in arm becomes at , so the difference between the height of two columns are .

In this case, restoring force acts on the liquid due to gravity. Acceleration of the liquid column, can be calculated in terms of restoring force.

Restoring force,

Weight of liquid column of height

Equilibrium level

As restoring force at opposite to gravitational force as liquid is lifted against

Then so motion is SHM.

Time period

Time period is independent of the density of the liquid and motion is harmonic.

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Question (5)

QN0038560

A particle is acted simultaneously by mutually perpendicular simple harmonic motion and . The trajectory of motion of the particle will be

(A)
an ellipse
(B)
a parabola
(C)
a circle
(D)
a straight line

Correct Answer: C

Explanation:

The resultant-displacement can be find by adding and -components.

According to variation of and , trajectory will be predicted, so resultant displacement is

As given that,

So,

So, the displacement is not straight line and not parabola also. Now, squaring and adding eqs. (i) and (ii),

This is the equation of a circle, so motion in circular (independent of time).

Clearly, the locus is a circle of constant radius .

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Question (6)

QN0038561

The displacement of a particle varies with time according to the relation .

(A)
The motion is oscillatory but not SHM
(B)
The motion is SHM with amplitude
(C)
The motion is SHM with amplitude
(D)
The motion is SHM with amplitude

Correct Answer: D

Explanation:

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Question (7)

QN0038562

Four pendulums  and  are suspended from the same elastic support as shown in figure.  and  are of the same length, while  is

smaller than  and  is larger than .
If  is given a transverse displacement,

(A)
will vibrate with maximum amplitude
(B)
will vibrate with maximum amplitude
(C)
will vibrate with maximum amplitude
(D)
All the four will oscillate with equal amplitude

Correct Answer: B

Explanation:

When pendulum vibrate with transverse vibration then

length of pendulum.

Through the elastic rigid support the disturbance is transferred to all the pendulum and are having length and hence same frequency. They will be in resonance, because their time period of oscillation.

So, a periodic force of period produces resonance in and and they will vibrate with maximum amplitude as in resonance.

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Question (8)

QN0038563

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 -projection of the
radius vector of the rotating particle is

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

Correct Answer: A

Explanation:

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Question (9)

QN0038564

The equation of motion of a particle is . The motion is

(A)
periodic but not oscillatory
(B)
periodic and oscillatory
(C)
oscillatory but not periodic
(D)
neither periodic nor oscillatory

Correct Answer: C

Explanation:

According to the question,

is a cosine function, so it is an oscillatory motion.

Now, at, . The equation of motion of particle

where, is supposed as period of the function .

Hence, it is oscillatory but not periodic.

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Question (10)

QN0038565

A particle executing SHM maximum speed of and a maximum acceleration of . The period of oscillation is

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

Correct Answer: A

Explanation:

Let us consider a equation of an SHM is represented by

(given) ...(i)

Acceleration

Eqs. (i) and (ii), we get

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Question (1)

The displacement of a particle is represented by the equation . The motion of the particle is

Explanation:

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Question (2)

The displacement of a particle is represented by the equation . The motion is

Explanation:

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Question (3)

The relation between acceleration and displacement of four particles are given below. Which, one of the particle is exempting simple harmonic motion?

Explanation:

Link:

Question (4)

Motion of an oscillating liquid column in a U-tube is

Explanation:

Link:

Question (5)

A particle is acted simultaneously by mutually perpendicular simple harmonic motion and . The trajectory of motion of the particle will be

Explanation:

Link:

Question (6)

The displacement of a particle varies with time according to the relation .

Explanation:

Link:

Question (7)

Four pendulums and are suspended from the same elastic support as shown in figure. and are of the same length, while is smaller than and is larger than .If is given a transverse displacement,

Explanation:

Link:

Question (8)

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 -projection of the radius vector of the rotating particle is

Explanation:

Link:

Question (9)

The equation of motion of a particle is . The motion is

Explanation:

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Question (10)

A particle executing SHM maximum speed of and a maximum acceleration of . The period of oscillation is

Explanation:

Link:

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OUR POLICY

Four pendulums and are suspended from the same elastic support as shown in figure. and are of the same length, while is

smaller than and is larger than .
If is given a transverse displacement,

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 -projection of the
radius vector of the rotating particle is