CBSE Questions for Class 11 Engineering Physics Oscillations Quiz 11 - MCQExams.com

A cubical block of side 'a' is floating in a fixed and closed cylindrical container of radius $$2a$$ kept on the ground. Density of the block is $$\rho$$, whereas the density of liquid is $$2\rho$$. Container is made up of conducting wall so that the temperature remains constant. A piston is mounted in the cylinder which can move inside the cylinder without friction. If piston oscillates with large amplitude A.
  • The cube will remain stationary
  • The cube will oscillate with very small amplitude in same phase with piston
  • The cube will oscillate with very small amplitude in opposite phase with piston
  • The cube will oscillate with amplitude A
(b) When the block is at position $$B$$ on the graph. its
  • position and velocity are positive
  • position is positive and velocity is negative
  • position in negative and velocity is positive
  • position and velocity are negative
When the block is at position $$C$$ on the graph, its
  • velocity is maximum and acceleration is zero
  • velocity if minimum and acceleration is zero
  • velocity is zero and acceleration is negative
  • velocity is zero and acceleration if positive
 (b) Position of the block as a function of time can now be expressed as
  • $$x=2\sqrt{3}\cos\left(16t+\dfrac{\pi}{6}\right)cm$$
  • $$x=3\cos\left(16t+\dfrac{\pi}{3}\right)cm$$
  • $$x=3.8\cos\left(16t+\dfrac{\pi}{6}\right)cm$$
  • $$x=3.2\cos \left(16t+\dfrac{\pi}{4}\right)cm$$
A particle executes SHM starting from its mean position at $$t=0$$. If its velocity is $$\sqrt 3 b\omega$$, when it is at a distance $$b$$ from the mean position, when $$\omega==2\pi /T$$, the time taken by the particle to move from $$b$$ to the extreme position on the same side is 
  • $$\dfrac{5\pi}{6\omega}$$
  • $$\dfrac{\pi}{3\omega}$$
  • $$\dfrac{\pi}{2\omega}$$
  • $$\dfrac{\pi}{4\omega}$$
A cork floating on the pond water executes a simple harmonic motion, moving up and down over a range of $$4\ cm$$. The time period of the motion is $$1\ s$$. At $$t=0$$, the cork is at its lowest position of oscillation, the position and velocity of the cork at $$t=10.5\ s$$, would be
  • $$2\ cm$$ above the mean position, $$0\ m/s$$
  • $$2\ cm$$ below the mean position, $$0\ m/s$$
  • $$1\ cm$$ above the mean position, $$2\sqrt 3 \pi \ m/s$$ up
  • $$1\ cm$$ below the mean position, $$2\sqrt 3 \pi \ m/s$$ up
A simple pendulum is oscillating between extreme positions $$P$$ and $$Q$$ about the mean position $$O$$. Which of the the following statements are true about the motion of pendulum?
  • At point $$O$$, the acceleration of the bob is difference from zero.
  • The acceleration of the bob is constant throughout the oscillation
  • The tension in the string is constant throughout the oscillation
  • The tension is maximum at $$O$$ and minimum at $$P$$ or $$Q$$
 (b) Velocity of the block as a function of time can be expressed as
1748913_3307bfbc3790412e88af2dfd3fcbde6a.png
  • $$v=-48\sin \left(16t\dfrac{\pi}{2}\right)cm/s$$
  • $$v=-48\sin \left(16t\dfrac{\pi}{3}\right)cm/s$$
  • $$v=-56\sin \left(16t\dfrac{\pi}{4}\right)cm/s$$
  • $$v=-56\sin \left(16t\dfrac{\pi}{6}\right)cm/s$$
The displacement of a particle is represented by the equation
$$y = 3 \cos \left [ \dfrac{\pi }{4} - 2\omega t  \right ]$$ the motion of the particle is 
  • Simple harmonic with period $$\dfrac{2\pi }{\omega } $$
  • Simple harmonic with period $$\dfrac{\pi }{\omega } $$
  • Periodic but not simple harmonic.
  • Non-periodic.
The displacement of a particle is represented by the equation $$y = \sin ^{3}\omega t$$ The motion is
  • non-periodic.
  • Periodic but not simple harmonic.
  • Simple harmonic with period $$\dfrac{2\pi }{\omega} $$
  • Simple harmonic with period $$\dfrac{\pi }{\omega} $$
Which of the following statements are true for a stationary wave?
  • Every particle has a fixed amplitude which is different from the amplitude of its nearest particle.
  • All the particles cross their mean position at the same time.
  • All the particles are oscillating with same amplitude.
  • There is no net transfer of energy across any plane.
  • There are some particles which are always at rest.
Which of the following statements is /are true for a simple harmonic oscillator?
  • Force acting is directly proportional to displacement from the mean position and opposite to it.
  • Motion is periodic.
  • Acceleration of the oscillator is constant.
  • The velocity is periodic.
A ball thrown by a boy from a roof-top has oscillatory motion.
  • True
  • False
Motion of a ball bearing inside a smooth curved bowl, when released from a point slightly above the lower point is
  • Simple harmonic motion.
  • Non-periodic motion.
  • Periodic motion.
  • Periodic but not SHM
The displacement time graph of a particle executing S.H.M. is shown in figure Which of the following statement is/are true?
1795089_61e59a24979040ceb9d3e4c16cb9430c.png
  • The force is zero at $$t = \dfrac{3 T}{4}$$
  • The acceleration is maximum at $$t = \dfrac{4 T}{4}$$
  • The velocity is maximum at $$t = \dfrac{T}{4}$$
  • The P.E. is equal to K.E. of oscillation at $$t = \dfrac{T}{2}$$
The relation acceleration and displacement of four particles are given below.
Which one particle is executing simple harmonic motion?
  • $$a_{x} = + 2x$$
  • $$a_{x} = 2x^{2}$$
  • $$a_{x} = - 2x^{2}$$
  • $$a_{x} = - 2x$$
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 
1795043_535af5490d154a2a8168906286faa3f9.png
  • $$x(t) = B \sin \left ( \dfrac{2 \pi t}{30} \right )$$
  • $$x(t) = B \cos \left ( \dfrac{\pi t}{15} \right )$$
  • $$x(t) = B \sin \left ( \dfrac{\pi t}{15} + \dfrac{\pi }{2} \right )$$
  • $$x(t) = B \cos \left ( \dfrac{\pi t}{15} + \dfrac{\pi }{2} \right )$$
Two masses $$m_1$$ and $$m_2$$ are suspended together by a massless springs of constant $$k$$. When the masses are in equilibrium, $$m_1$$ is removed without disturbing the system. Then the angular frequency of oscillation of $$m_2$$ is 
  • $$\sqrt{\dfrac{k}{m_1}}$$
  • $$\sqrt{\dfrac{k}{m_2}}$$
  • $$\sqrt{\dfrac{k}{m_1+m_2}}$$
  • $$\sqrt{\dfrac{k}{m_1m_2}}$$
What is constant in S.H.M.
  • Restoring force
  • Kinetic energy
  • Potential energy
  • Periodic time
A system exhibiting $$S.H.M$$ must possess
  • Inertia only
  • Elasticity as well as inertia
  • Elasticity inertia and an external force
  • Elasticity only
Which of the following is not true? In the case of a simple pendulum for small amplitudes the periodic of oscillation is
  • Directly proportional to square root of the length of the pendulum
  • Inversely proportional to square root of the acceleration due to gravity
  • Dependent on the mass, size and material of the bob
  • Independent of the amplitude
A mass $$m$$ is suspedend from the two coupled springs connected in series. The force constant for springs are $$K_1$$ and $$K_2$$. The time period of the suspended mass will be 
  • $$T=2\pi \sqrt{\left(\dfrac{m}{K_1+K_2}\right)}$$
  • $$T=2\pi \sqrt{\left(\dfrac{m}{K_1+K_2}\right)}$$
  • $$T=2\pi \sqrt{\left(\dfrac{m(K_1+K_2)}{K_1K_2}\right)}$$
  • $$T=2\pi \sqrt{\left(\dfrac{mK_1K_2}{K_1+K_2}\right)}$$
A simple pendulum is sec up in a trolley which moves to the right with an acceleration $$a$$ on a horizontal plane. Then the thread of the pendulum in the mean position makes an angle $$\theta$$ with the vertical
  • $$\tan^{-1} \dfrac ag$$ in the forward direction
  • $$\tan^{-1} \dfrac ag$$ in the backward direction
  • $$\tan^{-1} \dfrac ga$$ in the backrward direction
  • $$\tan^{-1} \dfrac ga$$ in the forward direction
The period of a simple pendulum is doubled, when 
  • Its length is doubled
  • The mass of the bob is doubled
  • Its length is made four times
  • The mass of the bob and the length of the pendulum are doubled
A particle moving along the $$x-$$axis execute simple harmonic motion, then the force acting on it is given by
  • $$-A\ Kx$$
  • $$A\ \cos \ (Kx)$$
  • $$A\ exp \ (-Kx)$$
  • $$A\ Kx$$
The period of simple pendulum is measured as $$T$$ in a stationary lift. If the lift moves upward with an acceleration of  $$5\ g$$, the period will be
  • The same
  • Increased by $$3/5$$
  • Decreased by $$2/3$$ times
  • None of the above
Mark the wrong statement
  • All S.H.M.s have fixed time period
  • All motion having same time period are S.H.M.
  • In S.H.M. total energy is proportional to square of amplitude
  • Phase constant of S.H.M. depends upon initial conditions
The time period of a simple pendulum is $$2$$ sec. If its length is increased $$4$$ times, then its period becomes
  • $$16$$ sec
  • $$12$$ sec
  • $$8$$ sec
  • $$4$$ sec
A block is placed on a frictionless horizontal table. The mass of the block is $$m$$ and springs are attached on either side with force constants $$K_1$$ and $$K_2$$. If the block is displaced a little and left to oscillate, then the angular frequency of oscillation will be 
  • $$\left( \dfrac{K_1+K_2}{m}\right)^{1/2}$$
  • $$\left[ \dfrac{K_1K_2}{m(K_1+K_2)}\right]^{1/2}$$
  • $$\left[ \dfrac{K_1K_2}{(K_1-K_2)m}\right]^{1/2}$$
  • $$\left[ \dfrac{K_1^2+K_2^2}{(K_1+K_2)m}\right]^{1/2}$$
In a simple pendulum, the period of oscillation $$T$$ is released to length of the pendulum $$l$$ as 
  • $$\dfrac {l}{T}=$$ constant
  • $$\dfrac {l^2}{T}=$$ constant
  • $$\dfrac {l}{T^2}=$$ constant
  • $$\dfrac {l^2}{T^2}=$$ constant
Graph between velocity and displacement of a particle, executing S.H.M. is
  • A straight line
  • A parabola
  • A hyperbola
  • An ellipse
If the length of simple pendulum is increased by $$300\%$$,then the time period will be increased by
  • $$100\%$$
  • $$200\%$$
  • $$300\%$$
  • $$400\%$$
A simple pendulum is executing simple harmonic motion with a time period $$T$$. If the length of the pendulum is increased by $$21\%$$, the percentage increase in the time period of the pendulum of increased length is
  • $$10\%$$
  • $$21\%$$
  • $$30\%$$
  • $$50\%$$
The force constants of two springs are $$K_1$$ and $$K_2$$. Both are stretched till their elastic energies are equal. If the stretching forces are $$F_1$$ and $$F_2$$, then $$F_1 : F_2$$ is 
  • $$K_1: K_2$$
  • $$K_2: K_1$$
  • $$\sqrt{K_1}: \sqrt{K_2}$$
  • $$K_1^2: K_2^2$$
If a simple harmonic oscillator has got a displacement of $$0.02\ m $$ and acceleration equal to $$2.0ms^{-2}$$ at any time, the angular frequency of the oscillator is equal to
  • $$10\ rad\ s^{-1}$$
  • $$0.1\ rad\ s^{-1}$$
  • $$100\ rad\ s^{-1}$$
  • $$1\ rad\ s^{-1}$$
What will be the force constant of the spring system shown in the figure 
1813698_13b7d9d276bf4e3590fc9361525d7534.png
  • $$\dfrac{K_1}{2}+K_2$$
  • $$\left[ \dfrac{1}{2K_1}+\dfrac{1}{K_2}\right]^{-1}$$
  • $$\dfrac{1}{2K_1}+\dfrac{1}{K_2}$$
  • $$\left[ \dfrac{2}{K_1}+\dfrac{1}{K_1}\right]^{-1}$$
A simple pendulum oscillates in air with time period $$T$$ and amplitude $$A$$. As the time passes
  • $$T$$ and $$A$$ both decrease
  • $$T$$ increases and $$A$$ is constant
  • $$T$$ increases and $$A$$ decreases
  • $$T$$ decreases and $$A$$ is constant
Two simple pendulum of length $$1.44\ m$$ and $$1\ m$$ start swinging together. After how many vibrates will they again start swinging together
  • $$5$$ oscillations of smaller pendulum
  • $$6$$ oscillations of smaller pendulum
  • $$4$$ oscillation of bigger pendulum
  • $$6$$ oscillation of bigger pendulum
A simple pendulum is set into vibrations. The bob of the pendulum comes to rest after some time due to
  • Air friction
  • Moment of inertia
  • Weight of the bob
  • Combination of all the above
The velocity of simple pendulum is maximum at 
  • Extremes
  • Half displacement
  • Mean position
  • Every where
The time period of simple pendulum when it is made to oscilate on the surface of moon
  • Increase
  • Decrease
  • Remains changed
  • Becomes infinite
On a planet a freely falling body takes $$2\ sec$$ when it is dropped from a height of $$8\ m$$, the time period of simple pendulum of length $$1\ m$$ on that planet is
  • $$3.14\ sec$$
  • $$6.28\ sec$$
  • $$1.57\ sec$$
  • None of these
A particle on the trough of a wave at any instant will come to the mean position after a time (t = time period)     [KCET 2005]
  • T/2
  • T/4
  • T
  • 2T
The graph shows variation of displacement of a particle performing S.H.M. with time t. which of the following statements is correct from the graph  ?
1841670_8dd064d68cbc4583b2c7cdcbb9263567.png
  • The acceleration is maximum at time T .
  • The force is maximum at time $$ \frac { 3T}{4} $$
  • The velocity is zero at time $$ \frac { T}{2 } $$
  • The kinetic energy is equal to total energy at a time $$ \frac {T}{4} $$
A set of keys on the end of a string is swung steadily in a horizontal circle. In one trial, it moves at speed $$v$$ in a circle of radius $$r$$. In a second trial, it moves at a higher speed $$4v$$ in a circle of radius $$4r$$. In the second trial, how does the period of its motion compare with its period in the first trial?
  • It is the same as in the first trial.
  • It is $$4$$ times larger.
  • It is one-fourth as large.
  • It is $$16$$ times larger.
  • It is one-sixteenth as large.
In the above question, the velocity of the rear 2 kg block after it separates from the spring will be :
  • 0 m/s
  • 5 m/s
  • 10 m/s
  • 7.5 m/s
A mass $$m$$ is undergoing SHM in the vertical direction about the mean position $$y_{0}$$ with amplitude A and angular frequency $$\omega$$. At a distance $$y$$ from the mean position, the mass detaches from the spring. Assume that the spring contracts and does not obstruct the motion of $$m$$. Find the distance $$y^{*}$$ (measured from the mean position) such that the height $$h$$ attained by the block is maximum. $$(\mathrm{A}\mathrm{\omega})^{2}>g$$

42890.jpg
  • $$\dfrac{g}{\omega^2}$$
  • $$\dfrac{2g}{\omega^2}$$
  • $$\dfrac{g}{2\omega^2}$$
  • None of these
A particle of mass m moves due to a conservative force with potential energy V(x) = $$\frac{Cx}{x^{2}+a^{2}}$$, where C and a are positive constants. The position(s) of stable equilibrium is/are given as
  • $$x = + a$$ only
  • $$x = - a$$ only
  • $$x = - \dfrac{a}{2}$$ and $$+ \dfrac{a}{2}$$
  • $$x = - a $$ and $$+ a $$
A particle of mass $$m$$ is bound by a linear potential $$U = Kr$$. It will have stationery circular motion with angular frequency $$\omega _{o}$$ with radius $$r$$ about the origin. If the particle is slightly disturbed from this circular motion, it will have small oscillations. If the angular frequency $$\omega$$ of the oscillations is $$\omega=\sqrt{n}\omega _{o}$$ The value of $$n$$ is :
  • $$2$$
  • $$3$$
  • $$5$$
  • $$6$$
A particle of mass m moves under a conservative force with potential energy. $$V(x)=\dfrac{ Cx}{\sqrt{a^2+x^2}, }$$ where $$C$$ and $$a$$are positive constants.
If the practicle starts from a point with velocity $$v$$, the range of values of $$v$$ for which it escapes to - $$\infty $$ are given by
  • v $$< \sqrt{\dfrac{C}{ma}}$$
  • v $$> \sqrt{\dfrac{C}{ma}}$$
  • v $$> \sqrt{\dfrac{2C}{ma}}$$
  • v $$< \sqrt{\dfrac{2C}{ma}}$$
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