(B) The block $P$ is carried along with block $Q$ due to the static friction force acting between them. The maximum static friction force available is

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(B) The block $P$ is carried along with block $Q$ due to the static friction force acting between them. The maximum static friction force available is $f_{max} = \mu N = \mu m_P g$,where $m_P$ is the mass of block $P$.The acceleration of the system is given by $a = -\omega^2 x$. The force required to keep block $P$ moving with block $Q$ is $F = m_P a = -m_P \omega^2 x$.Block $P$ will slip when the required force exceeds the maximum static friction,i.e.,$|m_P \omega^2 x| > \mu m_P g$,or $|x| > \frac{\mu g}{\omega^2}$.Since the acceleration magnitude $|a| = \omega^2 |x|$ is maximum at the extreme positions $(x = \pm A)$,the required force is maximum at these points. Therefore,block $P$ is most likely to slip at the extreme positions,$x = +A$ or $x = -A$.

Class 11 Physics Oscillations Mix Examples-Oscillations

Medium

In the figure shown,there is friction between the blocks $P$ and $Q$,but the contact between the block $Q$ and the lower surface is frictionless. Initially,the block $Q$ with block $P$ over it lies at $x=0$,with the spring at its natural length. The block $Q$ is pulled to the right and then released. As the spring-block system undergoes $S.H.M.$ with amplitude $A$,the block $P$ tends to slip over $Q$. $P$ is more likely to slip at:

A
$x=0$
B
$x=+A$
C
$x=+\frac{A}{2}$
D
$x=+\frac{A}{\sqrt{2}}$

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Class 11 Questions

Class 11

Physics Questions

Chapter

Oscillations

Subtopic

Mix Examples-Oscillations

State whether the following statements are True or False:
$1.$ If a spring is cut into two equal pieces,the spring constant of each piece decreases.
$2.$ As the displacement of a Simple Harmonic Oscillator $(SHO)$ increases,its acceleration decreases.
$3.$ $A$ system can oscillate with more than one natural frequency.
$4.$ The periodic time of Simple Harmonic Motion $(SHM)$ depends on amplitude,energy,or phase constant.

Medium

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Column $I$ gives a list of possible sets of parameters measured in some experiments. The variations of the parameters in the form of graphs are shown in Column $II$. Match the set of parameters given in Column $I$ with the graph given in Column $II$.

Column $I$ Column $II$

$(A)$ Potential energy of a simple pendulum ($y$-axis) as a function of displacement ($x$-axis) $(p)$ Parabolic curve opening upwards

$(B)$ Displacement ($y$-axis) as a function of time ($x$-axis) for a one-dimensional motion at zero or constant acceleration $(q)$ Linear graph passing through origin

$(C)$ Range of a projectile ($y$-axis) as a function of its velocity ($x$-axis) when projected at a fixed angle $(r)$ Linear graph with non-zero intercept

$(D)$ The square of the time period ($y$-axis) of a simple pendulum as a function of its length ($x$-axis) $(s)$ Parabolic curve opening upwards (starting from origin)

Column $I$	Column $II$
$(A)$ Potential energy of a simple pendulum ($y$-axis) as a function of displacement ($x$-axis)	$(p)$ Parabolic curve opening upwards
$(B)$ Displacement ($y$-axis) as a function of time ($x$-axis) for a one-dimensional motion at zero or constant acceleration	$(q)$ Linear graph passing through origin
$(C)$ Range of a projectile ($y$-axis) as a function of its velocity ($x$-axis) when projected at a fixed angle	$(r)$ Linear graph with non-zero intercept
$(D)$ The square of the time period ($y$-axis) of a simple pendulum as a function of its length ($x$-axis)	$(s)$ Parabolic curve opening upwards (starting from origin)

IIT 2008

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For a particle executing simple harmonic motion, match the following statements (conditions) from Column-$I$ to statements (shapes of graph) in Column-$II$.
Column-$I$ Column-$II$
$(A)$ Velocity-displacement graph $(\omega \neq 1)$ $(i)$ Straight line
$(B)$ Acceleration-displacement graph $(ii)$ Sinusoidal
$(C)$ Acceleration-time graph $(iii)$ Circle
$(D)$ Acceleration-velocity graph $(\omega \neq 1)$ $(iv)$ Ellipse

MediumAP EAMCET 2024

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$A$ clock $S$ is based on the oscillations of a spring,and a clock $P$ is based on pendulum motion. Both clocks run at the same rate on Earth. On a planet having the same density as Earth but twice the radius,then:

Medium

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$A$ particle is executing $SHM$ with an amplitude $A$ and angular frequency $\omega$. The ratio of the maximum acceleration to the maximum velocity of the particle is:

Medium

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Column-$I$	Column-$II$
$(A)$ Velocity-displacement graph $(\omega \neq 1)$	$(i)$ Straight line
$(B)$ Acceleration-displacement graph	$(ii)$ Sinusoidal
$(C)$ Acceleration-time graph	$(iii)$ Circle
$(D)$ Acceleration-velocity graph $(\omega \neq 1)$	$(iv)$ Ellipse

Similar Questions

$A$ clock $S$ is based on the oscillations of a spring,and a clock $P$ is based on pendulum motion. Both clocks run at the same rate on Earth. On a planet having the same density as Earth but twice the radius,then:

$A$ particle is executing $SHM$ with an amplitude $A$ and angular frequency $\omega$. The ratio of the maximum acceleration to the maximum velocity of the particle is:

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