Question

A spherical ball is dropped in a long column of a highly viscous liquid. The curve in the graph shown, which represents the speed of the ball (v) as a function of time (t) is:

• A. A
• B. B
• C. C
• D. D

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
When an object falls through a viscous fluid, it experiences three forces: weight (downward), buoyancy (upward), and viscous drag (upward).
Viscous drag is proportional to the velocity of the object (\(F_v \propto v\)).
Step 2: Detailed Explanation:
1. Initially, as the ball is dropped (\(u=0\)), the only forces are weight and buoyancy. Since weight is greater, the ball accelerates.
2. As the speed \(v\) increases, the upward viscous drag (\(6\pi\eta rv\)) also increases.
3. This reduces the net downward acceleration.
4. Eventually, the sum of buoyant force and viscous drag equals the weight. At this point, net force is zero, and the ball reaches a constant velocity called terminal velocity (\(v_t\)).
5. Graphically, this is represented by a curve that starts from the origin, increases with a decreasing slope, and eventually becomes a horizontal straight line.
Looking at the choices:
- Curve A is a straight line through the origin (constant acceleration), which is incorrect.
- Curve B shows the velocity increasing and then flattening out to a constant value, which correctly represents terminal velocity.
- Curves C and D do not follow this physical behavior.
Step 3: Final Answer:
The correct curve is B.