Question

A spherical object is falling under gravity through a viscous fluid. The sphere attains the terminal velocity when

• A. viscous force is zero.
• B. buoyant force is equal to force due to gravity
• C. viscous force plus force of gravity becomes equal to buoyant force.
• D. buoyant force plus viscous force becomes equal to force due to gravity.

Hint:

At terminal velocity the net force is zero.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
A sphere falling through a viscous fluid feels three forces. Gravity acts downward. The buoyant force and the viscous drag both act upward.

Step 2: Key Formula or Approach:
At terminal velocity the acceleration is zero, so the net force is zero: downward force equals upward forces.

Step 3: Detailed Explanation:
\(mg = F_{buoyant} + F_{viscous}\).
So the terminal velocity is reached when the buoyant force plus the viscous force equals the force due to gravity.
The viscous force is not zero at that instant, because it is the force that grows with speed until it balances the rest. Gravity must be on the opposite side of the equation from the other two forces.

Final Answer:
Terminal velocity is reached when buoyant force plus viscous force equals the force of gravity, option (D). \[ \boxed{\text{Buoyant force} + \text{viscous force} = \text{weight}} \]