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NEET 2006
Exam
NEET
Year
2006
Subject
Physics
Chapter
Mechanical Properties of Fluids

NEET 2006 · Physics · Mechanical Properties of Fluids

A rectangular block of mass m and area of cross-section A floats in...

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

Options

  1. AT∝1mT \propto \frac{1}{\sqrt{m}}
  2. BT∝AT \propto \sqrt{\mathrm{A}}
  3. CT∝1AT \propto \frac{1}{\sqrt{A}}
  4. DT∝1ρT \propto \frac{1}{\rho}

Correct answer

C. T∝1AT \propto \frac{1}{\sqrt{A}}

Step-by-step solution

Restoring force =A×∫g=kx=A \times \int g=k x ⇒K=Aρg⇒T=2πmAρg\begin{array}{ll} \Rightarrow & K=A \rho g \\ \Rightarrow & T=2 \pi \sqrt{\frac{m}{A \rho g}} \end{array} This shows that T∝1AT \propto \frac{1}{\sqrt{A}}.
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