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Q. No.

The time period of a spring mass system at the surface of the earth is \(2~\text{s}.\) What will be the time period of this system on the moon where the acceleration due to gravity is \(\frac{1}{16}^\text{th}\) of the value of \(g\) on the earth's surface?

1. \(\frac{1}{\sqrt{6}} ~\mathrm{s} \) 2. \(2 \sqrt{6}~ \mathrm{s} \)
3. \(2~ \mathrm{s} \) 4. \( 12~\mathrm{ s}\)

Subtopic:  Spring mass system |
 55%
Level 3: 35%-60%
Hints
If the displacement \(x\) and the velocity \(v\) of a particle executing simple harmonic motion are related through the expression \(4v^2= 25-x^2,\) then its time period will be:
1. \(\pi \) 2. \(2 \pi \)
3. \(4 \pi \) 4. \(6 \pi\)
Subtopic:  Linear SHM |
 68%
Level 2: 60%+
Hints

A simple pendulum is oscillating without damping. When the displacement of the bob is less than maximum, its acceleration vector \(\vec a\) is correctly shown in: 

1. 2.
3. 4.
Subtopic:  Angular SHM |
Level 3: 35%-60%
Hints
A particle executes SHM with an amplitude \(A\) and the time period \(T\). If at \(t=0,\) the particle is at its origin (mean position), then the time instant when it covers a distance equal to \(2.5A\) will be:
1. \( \frac{T}{12} \) 2. \(\frac{5 T}{12} \)
3. \( \frac{7 T}{12} \) 4. \(\frac{2 T}{3}\)
Subtopic:  Linear SHM |
 59%
Level 3: 35%-60%
Hints
The equations of the displacement of two particles making SHM are represented by \(y_1 = a\sin(\omega t + \phi)\) and \(y_2 = a\cos(\omega t)\) respectively. The phase difference of the velocities of the two particles will be:
1. \(\frac{\pi}{2}+\phi\)
2. \(-\phi\)
3. \(\phi\)
4. \(\phi-\frac{\pi}{2}\)
Subtopic:  Linear SHM |
 55%
Level 3: 35%-60%
Hints
If a particle is executing SHM, with an amplitude \(A,\) the distance moved and the displacement of the body in a time equal to its time period are, respectively:
1. \(2A,A\) 2. \(4A,0\)
3. \(A,A\) 4. \(0,2A\)
Subtopic:  Linear SHM |
 83%
Level 1: 80%+
Hints
The motion of a particle varies with time according to the relation \(y= a\sin\omega t+ a\cos \omega t\). Then:
1. the motion is oscillatory but not SHM.
2. the motion is SHM with an amplitude \(a\sqrt{2}\).
3. the motion is SHM with an amplitude \(\sqrt{2}\). 
4. the motion is SHM with an amplitude \(a\).
Subtopic:  Simple Harmonic Motion |
 73%
Level 2: 60%+
Hints
A particle is subjected to two simple harmonic motions in the same direction having equal amplitudes and equal frequency. If the resulting amplitude is equal to the amplitude of individual motions, the phase difference between them will be:
1. \(\frac{\pi}{3}\)
2. \(\frac{2\pi}{3}\)
3. \(\frac{\pi}{6}\)
4. \(\frac{\pi}{2}\)
Subtopic:  Linear SHM |
 63%
Level 2: 60%+
Hints
The variation of acceleration, \(a\) of a particle executing SHM with displacement \(x\) is:
1.     2.  
3.    4.   
Subtopic:  Simple Harmonic Motion |
 70%
Level 2: 60%+
Hints

A block \(P\) of mass \(m\) is placed on a frictionless horizontal surface. Another block \(Q\) of same mass is kept on \(P\) and connected to the wall with the help of a spring of spring constant \(k\) as shown in the figure. \(\mu_s\) is the coefficient of friction between \(P\) and \(Q\). The blocks move together performing SHM of amplitude \(A\). The maximum value of the friction force between \(P\) and \(Q\) will be:

         
1. \(kA\)
2. \(\frac{kA}{2}\)
3. zero
4. \(\mu_s mg\)

Subtopic:  Spring mass system |
Level 3: 35%-60%
Hints
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