A cylindrical block of wood (density $= 650\, kg\, m^{-3}$), of base area $30\,cm^2$ and height $54\, cm$, floats in a liquid of density $900\, kg\, m^{-3}$ . The block is depressed slightly and then released. The time period of the resulting oscillations of the block would be equal to that of a simple pendulum of length ..... $cm$ (nearly)
JEE MAIN 2015, Medium
Download our app for free and get started
Required equivalent length
$=\frac{\rho_{\text {wood }}}{\rho_{\text {liquid }}} \times$ height of block
$=\frac{650}{900} \times 54 \times 10^{-2}$
$\Rightarrow l=0.39 \mathrm{m}=39 \mathrm{cm}$
Download our appand 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
- 1A simple pendulum has time period $T$. The bob is given negative charge and surface below it is given positive charge. The new time period will beView Solution
- 2In the figure shown, there is friction between the blocks $P$ and $Q$ but the contact between the block $Q$ and lower surface is frictionless. Initially the block $Q$ with block $P$ over it lies at $x=0$, with spring at its natural length. The block $Q$ is pulled to right and then released. As the spring - blocks system undergoes $S.H.M.$ with amplitude $A$, the block $P$ tends to slip over $Q . P$ is more likely to slip atView Solution
- 3The position, velocity and acceleration of a particle executing simple harmonic motion are found to have magnitudes of $4 \mathrm{~m}, 2 \mathrm{~ms}^{-1}$ and $16 \mathrm{~ms}^{-2}$ at a certain instant. The amplitude of the motion is $\sqrt{\mathrm{x}} \mathrm{m}$ where $\mathrm{x}$ is. . . . . . .View Solution
- 4A light pointer fixed to one prong of a tuning fork touches a vertical plate. The fork is set vibrating and the plate is allowed to fall freely. If eight oscillations are counted when the plate falls through $10 cm$, the frequency of the tuning fork is .... $Hz$View Solution
- 5Vertical displacement of a plank with a body of mass $'m'$ on it is varying according to law $y = \sin \omega t + \cos \omega t.$ The minimum value of $\omega $ for which the mass just breaks off the plank and the moment it occurs first after $t = 0$ are given by : ( $y$ is positive vertically upwards)View Solution
- 6A particle executes $S.H.M$ between $x =\, -A$ to $x =\, +A$ . The time taken for it in going from $0$ to $A/2$ is $T_1$ and from $A/2$ to $A$ is $T_2$. ThenView Solution
- 7A particle is executing simple harmonic motion with an amplitude of $0.02$ metre and frequency $50\, Hz$. The maximum acceleration of the particle isView Solution
- 8A particle is executing $SHM$ of amplitude $A,$ about the mean position $x = 0.$ Which of the following cannot be a possible phase difference between the positions of the particle at $x = +\,A/2$ and $x = - A/\sqrt {2} .$View Solution
- 9A pendulum suspended from the ceiling of a train has a period $T$, when the train is at rest. When the train is accelerating with a uniform acceleration a, the period of oscillation willView Solution
- 10A particle moves on $x-$ axis according to the equation $x = x_0\,\,sin^2\,\omega t,$ the motion is simple harmonicView Solution