Download App
An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass $M$. The piston and the cylinder have equal cross sectional area $A$. When the piston is in equilibrium, the volume of the gas is $V_0$ and its pressure is $P_ 0$. The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency
  • A$\frac{1}{{2\pi }}\sqrt {\frac{{M{V_0}}}{{A\gamma {P_o}}}} \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;$
  • B$\;\frac{1}{{2\pi }}\sqrt {\frac{{A\gamma {P_o}}}{{{V_0}M}}} $
  • C$\;\frac{1}{{2\pi }}\sqrt {\frac{{{A^2}\gamma {P_o}}}{{M{V_0}}}} $
  • D$\;\frac{1}{{2\pi }}\frac{{{V_o}M{P_o}}}{{{A^2}\gamma }}$
JEE MAIN 2013, Diffcult
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.*
Download App

Similar Questions

  • 1
    In a simple pendulum, the period of oscillation $T$ is related to length of the pendulum $l$ as
    View Solution
  • 2
    A body of mass $1\,kg$ is executing simple harmonic motion. Its displacement $y(cm)$ at $t$ seconds is given by $y = 6\sin (100t + \pi /4)$. Its maximum kinetic energy is ..... $J$
    View Solution
  • 3
    Amplitude of a wave is represented by $A = \frac{c}{{a + b - c}}$ Then resonance will occur when
    View Solution
  • 4
    For a simple pendulum, a graph is plotted between its kinetic energy $(KE)$ and potential energy $(PE)$ against its displacement $d.$ Which one of the following represents these correctly ? (graphs are schematic and not drawn to scale)
    View Solution
  • 5
    The function of time representing a simple harmonic motion with a period of $\frac{\pi}{\omega}$ is :
    View Solution
  • 6
    A point particle of mass $0.1\, kg$ is executing $S.H.M$. of amplitude of $0.1\, m$. When the particle passes through the mean position, its kinetic energy is $8\times10^{-3}$ Joule. Obtain the equation of motion of this particle if this initial phase of oscillation is $45^o$.
    View Solution
  • 7
    A particle is placed at the lowest point of a smooth wire frame in the shape of a parabola, lying in the vertical $xy-$ plane having equation $x^2 = 5y$ $(x, y$ are in meter). After slight displacement, the particle is set free. Find angular frequency of oscillation.....$rad/s$  (in $rad/sec$ ) (take $g = 10\ m/s^2$ ) 
    View Solution
  • 8
    The displacement of a particle undergoing $SHM$ of time period $T$ is given by $x(t) = x_m\,cos\, (\omega t + \phi )$. The particle is at $x = -x_m$ at time $t = 0$. The particle is at $x = + x_m$ when
    View Solution
  • 9
    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
  • 10
    The metallic bob of a simple pendulum has the relative density $\rho$. The time period of this pendulum is $T$. If the metallic bob is immersed in water, then the new time period is given by
    View Solution