Question: 8: 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
(1) C
(2) D
(3) A
(4) B
Answer: Option (4)
Explanation:
When a spherical ball is dropped in a highly viscous liquid, three forces act on it:
gravitational force downward, buoyant force upward, and viscous drag force upward.
At the moment of release, the speed of the ball is zero, so the viscous force is zero.
The net force is maximum, and the ball starts accelerating downward.
As the speed increases, the viscous force, which is proportional to velocity, also increases.
This reduces the net force acting on the ball, and hence the acceleration gradually decreases.
After some time, the viscous force together with buoyant force balances the gravitational force.
At this stage, the net force becomes zero, acceleration becomes zero, and the ball attains a constant maximum speed called terminal velocity.
Thus, the speed–time graph starts from zero, increases rapidly at first, then gradually levels off and becomes constant with time.
Among the given curves, curve B shows an initially increasing velocity that gradually approaches a constant value, representing terminal velocity.
Hence, curve B correctly represents the motion of the ball in a highly viscous liquid.