A cylindrical plastic bottle of negligible ma | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The restoring force $F$ when the bottle is pushed down by a distance $x$ is given by the weight of the displaced water: $F = A \rho g x$,where $A

Vedclass · Accepted Answer

$7.9$

Vedclass · Answer

(B) The restoring force $F$ when the bottle is pushed down by a distance $x$ is given by the weight of the displaced water: $F = A ho g x$,where $A = \pi r^2$ is the cross-sectional area of the bottle.For simple harmonic motion,$F = m \omega^2 x$,where $m$ is the mass of the water inside the bottle.Equating the two: $\pi r^2 ho g x = m \omega^2 x$.Thus,$\omega = \sqrt{\frac{\pi r^2 ho g}{m}}$.Given $m = ho V$,where $V = 310\, ml = 310 	imes 10^{-6}\, m^3$ and $r = 2.5 	imes 10^{-2}\, m$.Substituting the values: $\omega = \sqrt{\frac{\pi r^2 ho g}{ho V}} = r \sqrt{\frac{\pi g}{V}}$.$\omega = (2.5 	imes 10^{-2}) \sqrt{\frac{3.14 	imes 10}{310 	imes 10^{-6}}} = (2.5 	imes 10^{-2}) \sqrt{\frac{31.4}{310 	imes 10^{-6}}} \approx (2.5 	imes 10^{-2}) \sqrt{10^5} \approx 2.5 	imes 316 	imes 10^{-2} \approx 7.9\, rad\, s^{-1}$.

Similar Questions

The angular velocity and the amplitude of a simple pendulum are $\omega$ and $A$ respectively. At a displacement $x$ from the mean position,its kinetic energy is $T$ and potential energy is $V$. Then the ratio $\frac{V}{T}$ is

$A$ simple pendulum with a bob of mass $m$ oscillates from $A$ to $C$ and back to $A$ such that $PB$ is $H$. If the acceleration due to gravity is $g$,then the velocity of the bob as it passes through $B$ is

Using a simple pendulum experiment, $g$ is determined by measuring its time period $T$. Which of the following plots represents the correct relation between the pendulum length $L$ and time period $T$?

$A$ chimpanzee swinging on a swing in a sitting position,stands up suddenly,the time period will

If the temperature of a pendulum with time period $T$ is increased by $\Delta \theta$,the change in the time period of the pendulum is .......

Vedclass Test Series

Exam Paper Generator

Online Exam Module