Q111 / 200 · NEET 2006 · Physics

A rectangular block of mass $m$ and area of cross-section A floats in a liquid of density $\rho$. If it is given a small vertical displacement from equilibrium it undergoes with a time period $T$, Then:

  • A
    $T \propto \frac{1}{\sqrt{m}}$
  • B
    $T \propto \sqrt{\mathrm{A}}$
  • Correct answer
    C
    $T \propto \frac{1}{\sqrt{A}}$
  • D
    $T \propto \frac{1}{\rho}$

Solution

Restoring force $=A \times \int g=k x$ $\begin{array}{ll} \Rightarrow & K=A \rho g \\ \Rightarrow & T=2 \pi \sqrt{\frac{m}{A \rho g}} \end{array}$ This shows that $T \propto \frac{1}{\sqrt{A}}$.

Hence, the correct answer is option: 'C'.

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