A light hollow cube of side length 10 cm and mass 10 g , is...

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 light hollow cube of side length 10 cm and mass 10 g , is floating in water. It is pushed down and released to

Options

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

Correct answer

B. $2$

Step-by-step solution

Additional buoyant force A light hollow cube of side length 10 cm and mass 10 g , is floating in water. It is pushed down and released to

\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}

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