Q130 / 180 · AIIMS 2004 · Physics

A sphere of mass $M$ and radius $R$ is falling in a viscous fluid. The terminal velocity attained by the falling object will be proportional to

  • Correct answer
    A
    $R^2$
  • B
    $R$
  • C
    $1 / R$
  • D
    $1 / R^2$.

Solution

Stoke's law : $6 \pi R \eta v=\frac{4}{3} \pi R^3(\rho-\sigma) g$ $\therefore \quad v \propto R^2$. As $M$ is given, $\rho=\frac{M}{\frac{4}{3} \pi R^3}$ But as $R^3$ increases, $M$ also increases and $\rho$ is a constant. $\sigma$ also is a constant. $\therefore \quad v$, the terminal velocity $\propto R^2$.

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

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