A block of rectangular size of mass $m$ and area of cross-section $A$, floats in a liquid of density $\rho$. If we give a small vertical displacement from equilibrium, it undergoes $S H M$ with time period $T$, then
AIIMS 2018, Diffcult
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
- 1The instantaneous displacement of a simple pendulum oscillator is given by $x = A\,\cos \,\left( {\omega t + \frac{\pi }{4}} \right)$ . Its speed will be maximum at timeView Solution
- 2A particle of mass $0.50 \mathrm{~kg}$ executes simple harmonic motion under force $\mathrm{F}=-50\left(\mathrm{Nm}^{-1}\right) \mathrm{x}$. The time period of oscillation is $\frac{x}{35} s$. The value of $x$ is . . . . .(Given $\pi=\frac{22}{7}$ )View Solution
- 3Two masses, both equal to $100\, g$, are suspended at the ends of identical light strings of length $\lambda = 1.0\, m$, attached to the same point on the ceiling (see figure). At time $t = 0$, they are simultaneously released from rest, one at angle $\theta_1 = 1^o$, the other at angle $\theta_2 = 2^o$ from the vertical. The masses will collideView Solution
- 4A particle executes simple harmonic motion along a straight line with an amplitude $A$. The potential energy is maximum when the displacement isView Solution
- 5A particle executes $SHM$ of period $1.2\, sec$ and amplitude $8\, cm.$ Find the time it takes to travel $3\,cm$ from the positive extremity of its oscillation. ..... $\sec$View Solution
- 6The motion of a particle varies with time according to the relation $y = a(\sin \omega \,t + \cos \omega \,t)$, thenView Solution
- 7The displacement of a particle varies according to the relation $x = 3 \ sin\ 100t + 8\ cos^2\ 50t$ . Which of the following is incorrect about this motionView Solution
- 8A $2\, Kg$ block moving with $10\, m/s$ strikes a spring of constant $\pi ^2 N/m$ attached to $2\, Kg$ block at rest kept on a smooth floor, the velocity of the rear $2\, kg$ block after it separates from the spring will be ..... $m/s$View Solution
- 9If displacement $x$ and velocity $v$ are related as $4v^2 = 16\, -\, x^2$ in a $SHM$ . Then time period of given $SHM$ is (consider $SI\,units$ )View Solution
- 10A pendulum is executing simple harmonic motion and its maximum kinetic energy is $K_1$. If the length of the pendulum is doubled and it performs simple harmonic motion with the same amplitude as in the first case, its maximum kinetic energy is $K_2$ thenView Solution