JEE Advanced Mix Test 34

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JEE Advanced Mix Test 34

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Weekly Quiz Competition

Question 1
4 / -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/T from the extreme position is :

A
a/T

B
2a/T

C
3a/T

D
a/2T

Solution
Question 2
4 / -1

A simple pendulum 50 cm long is suspended from the roof of a cart accelerating in the horizontal direction with constant acceleration √3 g m/s². The period of small oscillations of the pendulum about its equilibrium position is (g = π² m/s²) :

A
1.0 sec

B
√2 sec

C
1.53 sec

D
1.68 sec

Solution

With respect to the cart, equilibrium position of the pendulum is shown.If displaced by small angle θ from this position, then it will execute SHM about this equilibrium position, time period of which is given by:
Question 3
4 / -1

A particle is subjected to two simple harmonic motions along x and y directions according to, x = 3 sin 100 πt; y = 4 sin 100 πt:

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 π/2.

Solution
Question 4
4 / -1

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 p 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

Solution

Reflected pulse will be inverted as it is reflected by a denser medium. The wall exerts force in downward direction.
Question 5
4 / -1

The equation of displacement due to a sound wave is s = s₀sin² (ω t - kx). If the bulk modulus of the medium is B, then the equation of pressure variation due to that sound is:

A

B

C

D

Solution
Question 6
4 / -1

A point source of power 50π 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 π = 22/7) :

A
5 Nm^-2

B
10 Nm^-2

C
15 Nm^-2

D
20 Nm^-2

Solution
Question 7
4 / -1

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

Solution
Question 8
4 / -1

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

Solution

Two consecutive frequencies are 420 Hz & 480 Hz. So the fundamental frequency will be 60 Hz.
Question 9
4 / -1

A particle is executing SHM between points -X_m and X_m, 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 :

A
At time t₁ , it is going towards X_m.

B
At time t₁, its speed is decreasing.

C
At time t₂, its position lies in between –X_m and O.

D

Solution

At time t₁, velocity of the particle is negative i.e. going towards –Xm. From the graph, at time t₁, its speed is decreasing. Therefore particle lies in between –Xm and 0.

At time t₂, velocity is positive and its magnitude is less than maximum i.e. it has yet not crossed O.

It lies in between –Xm and 0.

Phase of particle at time t₁ is (180 + θ₁).

Phase of particle at time t₂ is (270 + θ₂)

Phase difference is 90 + (θ₂ – θ₁)

θ₂ – θ₁ can be negative making
Question 10
4 / -1

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.

Solution