A cylindrical plastic bottle of negligible mass of filled with $310\, ml$ of water and left floating in a pond with still water. If pressed downward slightly and released, it starts performing simple harmonic motion at angular frequency $\omega $. If the radius of the bottle is $2.5\, cm$ then $\omega $ is close to ..... $rad\, s^{-1}$ (density of water $= 10^3\, kg/m^3$)
JEE MAIN 2019, 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 displacement of a particle varies with time as $x = 12\sin \omega t - 16{\sin ^3}\omega t$ (in $cm$). If its motion is $S.H.M.$, then its maximum acceleration isView Solution
- 2The potential energy of a simple harmonic oscillator at mean position is $2\,joules$. If its mean $K.E.$ is $4\,joules$, its total energy will be .... $J$View Solution
- 3Figure shows the circular motion of a particle. The radius of the circle, the period, sense of revolution and the initial position are indicated on the figure. The simple harmonic motion of the $x-$ projection of the radius vector of the rotating particle $P$ isView Solution
- 4Two massless springs with spring constants $2\,k$ and $2\,k$, carry $50\, g$ and $100 \,g$ masses at their free ends. These two masses oscillate vertically such that their maximum velocities are equal. Then, the ratio of their respective amplitudes will beView Solution
- 5A block with mass $M$ is connected by a massless spring with stiffiess constant $k$ to a rigid wall and moves without friction on a horizontal surface. The block oscillates with small amplitude $A$ about an equilibrium position $x_0$. Consider two cases: ($i$) when the block is at $x_0$; and ($ii$) when the block is at $x=x_0+A$. In both the cases, a perticle with mass $m$ is placed on the mass $M$ ?View Solution
($A$) The amplitude of oscillation in the first case changes by a factor of $\sqrt{\frac{M}{m+M}}$, whereas in the second case it remains unchanged
($B$) The final time period of oscillation in both the cases is same
($C$) The total energy decreases in both the cases
($D$) The instantaneous speed at $x_0$ of the combined masses decreases in both the cases
- 6A particle executes $SHM$ with amplitude of $20 \,cm$ and time period is $12\, sec$. What is the minimum time required for it to move between two points $10\, cm$ on either side of the mean position ..... $\sec$ ?View Solution
- 7A particle is performing $SHM$ according to the equation $x = (3\, cm)$ $\sin \,\left( {\frac{{2\pi t}}{{18}} + \frac{\pi }{6}} \right)$ where $t$ is in seconds. The distance travelled by the particle in $36\, s$ is ..... $cm$View Solution
- 8A tunnel is dug in the earth across one of its diameter. Two masses $‘m’\,\& \,‘2m’$ are dropped from the ends of the tunnel. The masses collide and stick to each other and perform $S.H.M.$ Then amplitude of $S.H.M.$ will be : [$R =$ radius of the earth]View Solution
- 9Two identical balls A and B each of mass 0.1 kg are attached to two identical massless springs. The spring mass system is constrained to move inside a rigid smooth pipe bent in the form of a circle as shown in the figure. The pipe is fixed in a horizontal plane. The centres of the balls can move in a circle of radius 0.06 m. Each spring has a natural length of 0.06$\pi$ m and force constant 0.1N/m. Initially both the balls are displaced by an angle $\theta = \pi /6$ radian with respect to the diameter $PQ$ of the circle and released from rest. The frequency of oscillation of the ball B isView Solution
- 10A simple pendulum having length $\ell $ is having speed $\sqrt {2g\ell }$ at bottom most point of its trajectory. Its motion will beView Solution
