Question

If the terminal speed of a sphere of gold (density \(19.5 \, \text{g/cm}^3\)) is \(0.2 \, \text{m/s}\) in a viscous liquid (density \(1.5 \, \text{kg/m}^3\)), find the terminal speed of a sphere of silver (density \(10.5 \, \text{g/cm}^3\)) of the same size in the same liquid.

• A. \(0.4 \, \text{m/s}\)
• B. \(0.13 \, \text{m/s}\)
• C. \(1 \, \text{m/s}\)
• D. \(0.2 \, \text{m/s}\)

Hint:

The terminal velocity is inversely proportional to the density of the object. Higher density results in a lower terminal velocity.

Answer 1

The Correct Option is B

Step 1: Terminal Speed Relation.
The terminal speed for two objects in the same fluid can be found using the relation: \[ v_1 \propto \frac{d_1}{d_2} v_2 \] where \( v_1 \) and \( v_2 \) are the terminal velocities of the two spheres and \( d_1 \) and \( d_2 \) are their respective densities.
Step 2: Substituting Values.
For the two spheres (gold and silver), we use the given relation and substitute the densities. Solving for \( v_2 \) gives: \[ v_2 = 0.13 \, \text{m/s}. \] Step 3: Conclusion.
The correct answer is (B), \( 0.13 \, \text{m/s} \).