Question

A small metal sphere is falling through a viscous liquid. The variation of velocity (\(V\)) with time (\(t\)) is shown correctly in graph

• A. b
• B. a
• C. d
• D. c

Hint:

The sphere speeds up from rest and its speed levels off at terminal velocity.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
A sphere released in a viscous liquid has three forces: weight down, buoyancy up and viscous drag up. The drag grows with speed.

Step 2: Early motion
At the start the speed is zero, so the drag is zero. The net force is large, so the acceleration is large. The curve starts from the origin and rises steeply.

Step 3: Later motion
As the speed grows, the drag rises and the net force falls. The acceleration falls, so the curve bends over.

Step 4: Terminal velocity
Finally drag plus buoyancy equals weight, the net force is zero, and the speed stays constant at the terminal velocity. The graph becomes flat.

Step 5: Match the graphs
Graph (a) is constant speed from the start. Graph (b) is a straight line with a nonzero start. Graph (c) falls with time. Graph (d) rises from zero and flattens, which is what we found. So the answer is graph (d), option (C).

Final Answer:
The speed grows from zero and levels off at terminal velocity, which is graph (d), option (C). \[ \boxed{\text{graph (d)}} \]