$Assertion :$ In simple harmonic motion, the velocity is maximum when the acceleration is minimum.
$Reason :$ Displacement and velocity of $S.H.M.$ differ in phase by $\frac{\pi }{2}$
  • A
    If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.
  • B
    If both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion.
  • C
    If the Assertion is correct but Reason is incorrect.
  • D
    If both the Assertion and Reason are incorrect.
AIIMS 2014, Medium
art

Download our app
and get started for free

Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*

Similar Questions

  • 1
    The angular velocity and the amplitude of a simple pendulum is $'\omega '$ and $'A'$ respectively. At a displacement $x$ from the mean position its kinetic energy is $'T'$ and potnetial energy is $'V'$. Then the ratio $\frac{V}{T}$ is
    View Solution
  • 2
    When a particle of mass $m$ moves on the $x$-axis in a potential of the form $V(x)=\mathrm{kx}^2$ it performs simple harmonic motion. The corresponding time period is proportional to $\sqrt{\frac{\mathrm{m}}{\mathrm{k}}}$, as can be seen easily using dimensional analysis. However, the motion of a particle can be periodic even when its potential energy increases on both sides of $\mathrm{x}=0$ in a way different from $\mathrm{kx}^2$ and its total energy is such that the particle does not escape to infinity. Consider a particle of mass $\mathrm{m}$ moving on the $x$-axis. Its potential energy is $V(x)=\alpha x^4(\alpha>0)$ for $|x|$ near the origin and becomes a constant equal to $\mathrm{V}_0$ for $|x| \geq X_0$ (see figure). $Image$

    $1.$ If the total energy of the particle is $E$, it will perform periodic motion only if

    $(A)$ $E$ $<0$ $(B)$ $E$ $>0$ $(C)$ $\mathrm{V}_0 > \mathrm{E}>0$ $(D)$ $E > V_0$

    $2.$ For periodic motion of small amplitude $\mathrm{A}$, the time period $\mathrm{T}$ of this particle is proportional to

    $(A)$ $\mathrm{A} \sqrt{\frac{\mathrm{m}}{\alpha}}$ $(B)$ $\frac{1}{\mathrm{~A}} \sqrt{\frac{\mathrm{m}}{\alpha}}$ $(C)$ $\mathrm{A} \sqrt{\frac{\alpha}{\mathrm{m}}}$ $(D)$ $\mathrm{A} \sqrt{\frac{\alpha}{\mathrm{m}}}$

    $3.$ The acceleration of this particle for $|\mathrm{x}|>\mathrm{X}_0$ is

    $(A)$ proportional to $\mathrm{V}_0$

    $(B)$ proportional to $\frac{\mathrm{V}_0}{\mathrm{mX}_0}$

    $(C)$ proportional to $\sqrt{\frac{\mathrm{V}_0}{\mathrm{mX}_0}}$

    $(D)$ zero

    Give the answer qustion $1,2$ and $3.$

    View Solution
  • 3
    If the period of oscillation of mass $m$ suspended from a spring is $2\, sec$, then the period of mass $4m$ will be  .... $\sec$
    View Solution
  • 4
    What is the velocity of the bob of a simple pendulum at its mean position, if it is able to rise to vertical height of $10cm$  ......... $m/s$ (Take $g = 9.8\,m/{s^2})$
    View Solution
  • 5
    A particle executes $SHM.$ Its velocities are $v_1$and $v_2$ at displacement $x_1$ and $x_2$ from mean position respectively. The frequency of oscillation will be
    View Solution
  • 6
    A body executing simple harmonic motion has a maximum acceleration equal to $ 24\,metres/se{c^2} $ and maximum velocity equal to $ 16\;metres/sec $. The amplitude of the simple harmonic motion is
    View Solution
  • 7
    The potential energy of a particle executing S.H.M. is $ 2.5\, J$, when its displacement is half of amplitude. The total energy of the particle be .... $J$
    View Solution
  • 8
    A particle has simple harmonic motion. The equation of its motion is $x = 5\sin \left( {4t - \frac{\pi }{6}} \right)$, where $x$ is its displacement. If the displacement of the particle is $3$ units, then it velocity is
    View Solution
  • 9
    The piston in the cylinder head of locomotive has a stroke of $6\,m$ (which is twice the amplitude). If the piston executing simple harmonic motion with an angular frequency of $200\, rad\, min^{-1}$, its maximum speed is .... $ms^{-1}$
    View Solution
  • 10
    Two pendulums of length $121\,cm$ and $100\,cm$ start vibrating in phase. At some instant, the two are at their mean position in the same phase. The minimum number of vibrations of the shorter pendulum after which the two are again in phase at the mean position is :
    View Solution