Question 133: Oscillations

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 $$\omega $$ is close to – (density of water = 103 kg/m3).

Accepted Answer

Restoring force due to pressing the bottle with small
amount x,
F = $$ - \left( {ho Ax} ight)g$$
$$ \Rightarrow $$ ma = $$ - \left( {ho Ax} ight)g$$
$$ \Rightarrow $$ a = $$ - \left( {{{ho Ag} \over m}} ight)x$$
$$ 	herefore $$ $${{\omega ^2} = {{ho Ag} \over m}}$$ = $${{{ho \left( {\pi {r^2}} ight)g} \over m}}$$
$$ \Rightarrow $$ $$\omega $$ = $$\sqrt {{{{{10}^3} 	imes \pi  	imes {{\left( {2.5 	imes {{10}^{ - 2}}} ight)}^2} 	imes 10} \over {310 	imes {{10}^{ - 3}}}}} $$ = 7.90 rad/s

Answer

2.50 rad s$$-$$1

Answer

3.75 rad s$$-$$1

Answer

5.00 rad s$$-$$1

Answer

7.90 rad s$$-$$1

Oscillations

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