Question

A spherical ball of radius \( 1 \times 10^{-4} \) m and density \( 10^4 \) kgm\(^{-3}\) falls freely under gravity before entering water. The distance \( h \) before velocity change in water is:

• A. \( 20.4 \) cm
• B. \( 20.4 \) mm
• C. \( 20.4 \) m
• D. \( 10.2 \) m

Hint:

For spheres in fluid, use Stoke’s Law to determine velocity and displacement.

Answer 1

The Correct Option is C

Step 1: Using Stoke’s Law The velocity before entering water: \[ v = \sqrt{\frac{2gh}{1 - \rho_f / \rho}} \] Solving, we get: \[ h = 20.4 m \] Thus, the correct answer is option (3).