Question 152 of 194

A light hollow cube of side length 10 cm and mass 10 g , is floating in water. It is pushed down and released to execute simple harmonic oscillations. The time period of oscillations is $y \pi \times 10^{-2} \mathrm{~s}$, where the value of $y$ is
(Acceleration due to gravity, $g=10 \mathrm{~m} / \mathrm{s}^2$, density of water $=10^3 \mathrm{~kg} / \mathrm{m}^3$ )

A$6$B$2$C$4$D$1$

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Answer: (B) $2$

Additional buoyant force


$\begin{aligned}
& g \rho a^2 x=\sigma a^3 A \\
& A=\frac{\rho}{\sigma} \frac{g}{a} x \\
& T=2 \pi \sqrt{\frac{\sigma a}{\rho g}}
\end{aligned}$

Now, $\sigma=\frac{10 \times 10^{-3}}{10^{-3}}=10$
$\begin{aligned} \Rightarrow \quad T & =2 \pi \sqrt{\frac{10 \times 0.1}{10^3 \times 10}} \\ & =2 \pi \times 10^{-2}\end{aligned}$