question_answer

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 co. If the radius of the bottle is 2.5 cm then co is close to - (density of water\[={{10}^{3}}kg/{{m}^{3}}\]).      [JEE Main 10-Jan-2019 Evening]

A)  \[2.50\text{ }rad\text{ }{{s}^{-}}^{1}\]         

B)       \[3.75\text{ }rad\text{ }{{s}^{-1}}\]

C)  \[5.00\text{ }rad\text{ }{{s}^{-1}}\]    

D)      None of these

Correct Answer: D

Solution :

[d] (Bonus)

On depressed slightly restoring force

Mass of bottle with water in it, \[=\text{ }V\times {{\rho }_{water}}\]

\[=\,\,\,310\times {{10}^{-}}^{6}\times {{10}^{3+}}\]

\[=\text{ }0.31\text{ }kg\]

\[0.31\text{ }a=A{{\rho }_{water}}\,x\times 10\]

\[a=\pi {{\left( \frac{2.5}{100} \right)}^{2}}\,\times \frac{10\times 10}{0.31}x\]

\[=\,\,\frac{3.1}{0.31}\,\times \,\frac{{{(2.5)}^{2}}\,\times \,{{10}^{4}}}{{{10}^{4}}}x\]

\[a=10\,\times \,{{\left( 2.5 \right)}^{2}}x\]

\[a=62.5\text{ }x\]

\[\omega =\sqrt{62.5}\text{ }rad/s\]

\[\omega =8\text{ }rad/s\]

as no answer is matching.