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Physics · MECHANICAL PROPERTIES OF FLUIDS

हिन्दी

A copper ball of radius \( 2.0\text{ mm} \) falls through a large column of oil at \( 20^\circ\text{C} \) with a terminal speed of \( 6.5\text{ cm/s} \). The density of copper is \( 8.9 \times 10^3\text{ kg/m}^3 \) and that of oil is \( 1.5 \times 10^3\text{ kg/m}^3 \). Taking \( g = 9.8\text{ m/s}^2 \), the viscous drag force acting on the ball at terminal speed is approximately:

  1. A
    \( 4.8 \times 10^{-3}\text{ N} \)
  2. B
    \( 1.2 \times 10^{-3}\text{ N} \)
  3. C
    \( 2.4 \times 10^{-3}\text{ N} \)
  4. D
    \( 3.6 \times 10^{-3}\text{ N} \)
View Answer & Solution

Correct answer · Option C

\( 2.4 \times 10^{-3}\text{ N} \)

Explanation

At terminal speed, net force is zero: viscous force \( F_{\text{v}} = \frac{4}{3}\pi a^3 (\rho - \sigma)g = \frac{4}{3}\pi (2 \times 10^{-3})^3 (8.9 - 1.5) \times 10^3 \times 9.8 \approx \frac{4}{3}(3.14)(8 \times 10^{-9})(7.4 \times 10^3)(9.8) \approx 2.43 \times 10^{-3}\text{ N} \).
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