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-1Option 3)1.25 rad s-1Option 4)3.75 rad s-1

A anshigandhi
1. 5tg456ggfffffffffffffffffff55t3t2rdwsx

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)

Option 2)