Question

The terminal velocity of a small steel ball of radius \(r\) falling in a fluid is proportional to

• A. \(r^8\)
• B. \(r^7\)
• C. \(r^2\)
• D. \(r^1\)
• E. \(r^5\)

Hint:

By Stokes’ law, terminal velocity of a small sphere in a viscous fluid varies as: \[ v_t\propto r^2 \]

Answer 1

The Correct Option is C

For a small sphere falling through a viscous fluid, terminal velocity is given by Stokes’ law: \[ v_t=\frac{2r^2(\rho-\sigma)g}{9\eta} \] where:

• \(r\) is the radius of the sphere,
• \(\rho\) is density of the sphere,
• \(\sigma\) is density of the fluid,
• \(\eta\) is coefficient of viscosity.

From this formula: \[ v_t \propto r^2 \]
Hence, the correct answer is the option corresponding to: \[ \boxed{r^2} \]