# Q. 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 $\omega$ close to : (density of water = $10^3 \; kg / m^3$)

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Solution:

## Extra Boyant force = $\delta$ Axg $B_0 + B \times \; mg = ma$ $B= ma$ $a =\left(\frac{\delta Ag}{m}\right)^{x}$ $w^{2} =\frac{\delta Ag}{m}$ $w = \sqrt{\frac{10^{3} \times\pi\left(2.5\right)^{2} \times10^{-4} \times10}{310 \times10^{-6} \times10^{3}}}$ $= \sqrt{63.30} = 7.95$

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