Question 109: 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 = 10
3
kg/m
3
).

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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