A cylindrical block of density $\rho$ is partially immersed in a liquid of density $3\rho .$ The plane surface of the block remains parallel to the surface of the liquid. The height of the block is $60\, cm.$ The block performs $SHM$ when displaced from its mean position. [Use $ g = 9.8\, m/s^2$]
  • Athe maximum amplitude is $20 \,cm$
  • Bthe maximum amplitude is $40 \,cm$
  • Cthe time period will be $2\pi /7$ seconds.
  • D$(A)$ and $(C)$ both
Advanced
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 displacement of a particle moving in $S.H.M.$ at any instant is given by $y = a\sin \omega t$. The acceleration after time $t = \frac{T}{4}$ is (where $T$ is the time period)
    View Solution
  • 2
    A particle starts with $S.H.M.$ from the mean position as shown in the figure. Its amplitude is $A$ and its time period is $T$. At one time, its speed is half that of the maximum speed. What is this displacement?
    View Solution
  • 3
    The period of small oscillation of a simple pendulum is $T$. The ratio of density of liquid to the density of material of the bob is $\rho \left( {\rho  < 1} \right)$.When immersed in the liquid, the time period of small oscillation will now be
    View Solution
  • 4
    A pendulume clock loses $12\;s$ a day if the temperature is $40^oC$ and gains $4\;s$ a day if the temperature is $20^oC$. The temperature at which the clock will show correct time, and the coeffecient of linear expansion $(\alpha)$ of the metal of the pendulum shaft are respectively
    View Solution
  • 5
    In the arrangement, spring constant $k$ has value $2\,N\,m^{-1}$ , mass $M = 3\,kg$ and mass $m = 1\,kg$ . Mass $M$ is in contact with a smooth surface. The coefficient of friction between two blocks is $0.1$ . The time period of $SHM$ executed by the system is
    View Solution
  • 6
    Two particles are executing simple harmonic motion of the same amplitude $A$ and frequency $\omega $ along the $x-$ axis. Their mean position is separated by distance $X_0 (X_0> A)$. If the maximum separation between them is $(X_0 +A)$, the phase difference between their motion is
    View Solution
  • 7
    A pendulum with time period of $1\, s$ is losing energy due to damping. At certain time its energy is $45\, J$. If after  completing $15\,oscillations$ , its energy has become $15\, J$, its damping constant (in $s^{-1}$ ) is
    View Solution
  • 8
    When the displacement is half the amplitude, the ratio of potential energy to the total energy is
    View Solution
  • 9
    Two springs of force constants $300\, N/m$ (Spring $A$) and $400\, N/m$ (Spring $B$) are joined together in series . The combination is compressed by $8.75\, cm$. The ratio of energy stored in $A$ and $B$ is  $\frac{{{E_A}}}{{{E_B}}}$.  Then $\frac{{{E_A}}}{{{E_B}}}$ is equal to
    View Solution
  • 10
    The equation of a particle executing simple harmonic motion is given by $x =\sin \pi\left( t +\frac{1}{3}\right) m$. At $t =1 \,s$, the speed of particle will be .......... $cm s ^{-1}$ (Given : $\pi=3.14$ )
    View Solution