Which one of the following graphs represents the velocity-time ($v-t$) graph of a small spherical body falling in a viscous liquid?
To determine the correct velocity-time graph representing a small spherical body falling in a viscous liquid, we need to understand the physics of the scenario.
- The body experiences two main forces: gravitational force pulling it downwards and a viscous drag force opposing its motion.
- Initially, when the body starts falling, the gravitational force is dominant, and the velocity of the body increases.
- As the velocity increases, the viscous drag force also increases, which acts opposite to the gravitational force. This results in a net force that gradually decreases.
- Eventually, the body reaches a terminal velocity where the gravitational force equals the viscous drag force. At this point, the net force is zero, and thus the acceleration is zero.
- When the body reaches terminal velocity, it falls with a constant velocity.
From the above reasoning, the velocity-time graph should depict an initial increase in velocity followed by a constant velocity after some time.
The correct graph is the first option, where the velocity initially increases and then becomes constant, indicating the body has reached terminal velocity.
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