Question

A cylindrical plastic bottel of negligible mass is filled with 310 ml of water and left floating in a pound 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. $5.00rad{s}^{-1}$
• B. $1.25rad{s}^{-1}$
• C. $3.75rad{s}^{-1}$
• D. $7.95rad{s}^{-1}$

Answer 1

Answer: (D)

$7.95rad{s}^{-1}$

Extra Boyant force = $\delta Axg$

$B_o+B\times mg=ma$

B = ma

$a=\left(\frac{\delta Ag}{m}\right)$

$w^2=\frac{\delta Ag}{m}$

$w=\sqrt{\frac{{10}^3\times \pi (2.5{)}^2\times {10}^{-4}\times 10}{310\times {10}^{-}6\times {10}^3}}=\sqrt{63.30}=7.95rad{s}^{-1}$