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  • Confused! kindly explain, - A cylindrical plastic bottle of negligible mass is filled with 310 ml of water and left floating in - Oscillations and Waves - JEE Main

A cylindrical plastic bottle of negligible mass is 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 : (density of water = 103 Kg/m3)

 

  • Option 1)

    5.00 rad s-1

     

  • Option 2)

    2.50 rad s-1

  • Option 3)

    1.25 rad s-1

  • Option 4)

    3.75 rad s-1

Answers (2)

best_answer

 

Equation of S.H.M. -

a=-\frac{d^{2}x}{dt^{2}}= -w^{2}x

w= \sqrt{\frac{k}{m}}

 

- wherein

x= A\sin \left ( wt+\delta \right )

A \times \rho g=F_{res}\Rightarrow \left ( \pi r^{2}\rho g \right )\times =F_{rest}

\omega ^{2} = \frac{\pi r^{2}\rho g}{m}\Rightarrow \omega =r\sqrt{\frac{\pi g}{v}}

since m =\rho V

\omega =2.5\times 10^{-2}\sqrt{\frac{3.14\times 10}{310\times 10^{-6}}} = 2.5\sqrt{10}

 

 


Option 1)

5.00 rad s-1

 

Option 2)

2.50 rad s-1

Option 3)

1.25 rad s-1

Option 4)

3.75 rad s-1

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