Question

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 = $10^3 \; kg / m^3$)

• A. $5.00 \; rad \; s^{-1}$
• B. $1.25 \; rad \; s^{-1}$
• C. $3.75 \; rad \; s^{-1}$
• D. $2.5\sqrt{10} \; rad \; s^{-1}$

Answer 1

Answer: (D)

$2.5\sqrt{10} \; rad \; s^{-1}$

Answer 2

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