NEET
- Exam
- NEET
- Subject
- Physics
- Chapter
- Mechanical Properties of Fluids
NEET · Physics · Mechanical Properties of Fluids
A tiny spherical glass bead is projected vertically downwards into...
A tiny spherical glass bead is projected vertically downwards into a deep column of highly viscous oil. Its initial downward velocity is twice its terminal velocity (). Which of the following descriptions correctly shows the variation of its velocity () with time ()?
Options
- AA curve starting at on the velocity axis and decreasing with a continuously flattening slope to approach a horizontal asymptote at .
- BA curve starting at on the velocity axis and decreasing continuously to approach zero asymptotically.
- CA straight line starting at on the velocity axis and decreasing linearly until it abruptly becomes horizontal at .
- DA curve starting at on the velocity axis and increasing with a continuously flattening slope to approach a higher horizontal asymptote.
Correct answer
A. A curve starting at on the velocity axis and decreasing with a continuously flattening slope to approach a horizontal asymptote at .
Step-by-step solution
The net downward force on the spherical bead is given by , where is the effective weight (weight minus buoyancy) is the velocity-dependent viscous drag.
At terminal velocity , the net force is zero, so .
The bead is projected with an initial velocity . Since , the initial upward viscous drag is greater than the downward effective weight.
This results in a net upward force, causing the bead to decelerate. As the velocity decreases, the viscous drag decreases, and the net upward force (and thus the retardation) decreases.
The velocity will continuously decrease from and asymptotically approach the terminal velocity from above. The graph is a curve starting at and flattening out to a horizontal asymptote at .
Answer: A curve starting at on the velocity axis and decreasing with a continuously flattening slope to approach a horizontal asymptote at .
At terminal velocity , the net force is zero, so .
The bead is projected with an initial velocity . Since , the initial upward viscous drag is greater than the downward effective weight.
This results in a net upward force, causing the bead to decelerate. As the velocity decreases, the viscous drag decreases, and the net upward force (and thus the retardation) decreases.
The velocity will continuously decrease from and asymptotically approach the terminal velocity from above. The graph is a curve starting at and flattening out to a horizontal asymptote at .
Answer: A curve starting at on the velocity axis and decreasing with a continuously flattening slope to approach a horizontal asymptote at .