A cylindrical plastic bottle of negligible mass is filled with 310 ml… | JEE Main 2019 (10 Jan, Shift 2)

Q14JEE Main 2019 · 10 JAN · SHIFT 2Medium

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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).

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Answer: (d)

$\omega = \sqrt{\frac{\rho A g}{m}}$ with $m = 0.31\text{ kg}$ , $A = \pi(0.025)^2 = 1.96 \times 10^{-3}\text{ m}^2$ .
$\omega = \sqrt{\frac{10^3 \times 1.96 \times 10^{-3} \times 9.8}{0.31}} = \sqrt{62} \approx 7.9\text{ rad/s}$
So the answer is (d).

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