ExamBro
ExamBro
MHT CET · Physics · Mechanical Properties of Fluids

A steel ball of radius 6 mm has a terminal speed of \(12 \mathrm{cms}^{-1}\) in a viscous liquid. What will be the terminal speed of a steel ball of radius 3 mm in the same liquid?

  1. A \(12 \mathrm{cms}^{-1}\)
  2. B \(9 \mathrm{cms}^{-1}\)
  3. C \(6 \mathrm{cms}^{-1}\)
  4. D \(3 \mathrm{cms}^{-1}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(3 \mathrm{cms}^{-1}\)

Step-by-step Solution

Detailed explanation

Terminal speed,
\(v=\frac{2 r^2 g\left(\rho-\rho_L\right)}{9 \eta}\)
Since density of balls and liquid remains the same,
\(\begin{aligned}
& \therefore \quad \frac{\mathrm{v}_{\mathrm{A}}}{\mathrm{v}_{\mathrm{B}}}=\left(\frac{\mathrm{r}_{\mathrm{A}}}{\mathrm{r}_{\mathrm{B}}}\right)^2=\left(\frac{6}{3}\right)^2=4 \\
& \therefore \quad \mathrm{v}_{\mathrm{B}}=\frac{\mathrm{v}_{\mathrm{A}}}{4}=\frac{12}{4}=3 \mathrm{cms}^{-1}
\end{aligned}\)