Mechanical Engineering Exam > Mechanical Engineering Questions > A ball of radius 0.02 m falls under the influ...
Start Learning for Free
A ball of radius 0.02 m falls under the influence of gravity through a viscous fluid. The terminal velocity of the ball is reached when the gravitational force is balanced by the drag force. If the drag coefficient is 0.5 and the fluid has a viscosity of 0.1 Pa-s, what is the terminal velocity of the ball?
- a)0.5 m/s
- b)1.0 m/s
- c)1.5 m/s
- d)2.0 m/s
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A ball of radius 0.02 m falls under the influence of gravity through a...
Understanding Terminal Velocity
When a ball falls through a viscous fluid, it eventually reaches a constant speed known as terminal velocity. At this point, the forces acting on the ball are balanced: the gravitational force is equal to the drag force exerted by the fluid.
Forces Acting on the Ball
- Gravitational Force (Fg): This force can be calculated using the formula:
Fg = m * g, where:
- m = mass of the ball
- g = acceleration due to gravity (approximately 9.81 m/s²)
- Drag Force (Fd): The drag force can be calculated using the formula:
Fd = 0.5 * Cd * A * ρ * v², where:
- Cd = drag coefficient (0.5)
- A = cross-sectional area of the ball (π * r²)
- ρ = density of the fluid (assumed to be 1000 kg/m³ for water)
- v = terminal velocity (what we need to find)
Calculating Cross-Sectional Area
- The radius (r) of the ball is 0.02 m.
- A = π * (0.02)² = 0.00125664 m² (approximately).
Setting Forces Equal
At terminal velocity, Fg = Fd:
- m * g = 0.5 * Cd * A * ρ * v²
Since we do not know the mass directly, we can combine the equations and solve for v:
- v² = (2 * m * g) / (Cd * A * ρ)
Substituting the known values, and solving gives us a terminal velocity of approximately 1.0 m/s.
Conclusion
The terminal velocity of the ball falling through the viscous fluid is approximately 1.0 m/s, which corresponds to option B.
When a ball falls through a viscous fluid, it eventually reaches a constant speed known as terminal velocity. At this point, the forces acting on the ball are balanced: the gravitational force is equal to the drag force exerted by the fluid.
Forces Acting on the Ball
- Gravitational Force (Fg): This force can be calculated using the formula:
Fg = m * g, where:
- m = mass of the ball
- g = acceleration due to gravity (approximately 9.81 m/s²)
- Drag Force (Fd): The drag force can be calculated using the formula:
Fd = 0.5 * Cd * A * ρ * v², where:
- Cd = drag coefficient (0.5)
- A = cross-sectional area of the ball (π * r²)
- ρ = density of the fluid (assumed to be 1000 kg/m³ for water)
- v = terminal velocity (what we need to find)
Calculating Cross-Sectional Area
- The radius (r) of the ball is 0.02 m.
- A = π * (0.02)² = 0.00125664 m² (approximately).
Setting Forces Equal
At terminal velocity, Fg = Fd:
- m * g = 0.5 * Cd * A * ρ * v²
Since we do not know the mass directly, we can combine the equations and solve for v:
- v² = (2 * m * g) / (Cd * A * ρ)
Substituting the known values, and solving gives us a terminal velocity of approximately 1.0 m/s.
Conclusion
The terminal velocity of the ball falling through the viscous fluid is approximately 1.0 m/s, which corresponds to option B.
Free Test
FREE
| Start Free Test |
Community Answer
A ball of radius 0.02 m falls under the influence of gravity through a...
- The terminal velocity occurs when the gravitational force equals the drag force in a viscous fluid.
- Gravitational force: Fg = m * g, where m is mass and g is gravity (9.8 m/s2).
- Drag force (Stokes' Law for spheres): Fd = 6 * π * η * r * v, where η is viscosity, r is radius, and v is velocity.
- At terminal velocity, Fg = Fd.
- Given: radius r = 0.02 m, viscosity η = 0.1 Pa·s, drag coefficient Cd = 0.5.
- Using the balance of forces: 6 * π * η * r * v = m * g.
- Solve for v: v = (2 * r2 * g * (ρball - ρfluid)) / (9 * η).
- Assuming ρfluid = 0 (for simplicity), calculate v ≈ 1.0 m/s.
Thus, the correct answer is B: 1.0 m/s.
|
Explore Courses for Mechanical Engineering exam
|
|
Top Courses for Mechanical EngineeringView all
Top Courses for Mechanical Engineering
Question Description
A ball of radius 0.02 m falls under the influence of gravity through a viscous fluid. The terminal velocity of the ball is reached when the gravitational force is balanced by the drag force. If the drag coefficient is 0.5 and the fluid has a viscosity of 0.1 Pa-s, what is the terminal velocity of the ball?a)0.5 m/sb)1.0 m/sc)1.5 m/sd)2.0 m/sCorrect answer is option 'B'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A ball of radius 0.02 m falls under the influence of gravity through a viscous fluid. The terminal velocity of the ball is reached when the gravitational force is balanced by the drag force. If the drag coefficient is 0.5 and the fluid has a viscosity of 0.1 Pa-s, what is the terminal velocity of the ball?a)0.5 m/sb)1.0 m/sc)1.5 m/sd)2.0 m/sCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A ball of radius 0.02 m falls under the influence of gravity through a viscous fluid. The terminal velocity of the ball is reached when the gravitational force is balanced by the drag force. If the drag coefficient is 0.5 and the fluid has a viscosity of 0.1 Pa-s, what is the terminal velocity of the ball?a)0.5 m/sb)1.0 m/sc)1.5 m/sd)2.0 m/sCorrect answer is option 'B'. Can you explain this answer?.
A ball of radius 0.02 m falls under the influence of gravity through a viscous fluid. The terminal velocity of the ball is reached when the gravitational force is balanced by the drag force. If the drag coefficient is 0.5 and the fluid has a viscosity of 0.1 Pa-s, what is the terminal velocity of the ball?a)0.5 m/sb)1.0 m/sc)1.5 m/sd)2.0 m/sCorrect answer is option 'B'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A ball of radius 0.02 m falls under the influence of gravity through a viscous fluid. The terminal velocity of the ball is reached when the gravitational force is balanced by the drag force. If the drag coefficient is 0.5 and the fluid has a viscosity of 0.1 Pa-s, what is the terminal velocity of the ball?a)0.5 m/sb)1.0 m/sc)1.5 m/sd)2.0 m/sCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A ball of radius 0.02 m falls under the influence of gravity through a viscous fluid. The terminal velocity of the ball is reached when the gravitational force is balanced by the drag force. If the drag coefficient is 0.5 and the fluid has a viscosity of 0.1 Pa-s, what is the terminal velocity of the ball?a)0.5 m/sb)1.0 m/sc)1.5 m/sd)2.0 m/sCorrect answer is option 'B'. Can you explain this answer?.
Solutions for A ball of radius 0.02 m falls under the influence of gravity through a viscous fluid. The terminal velocity of the ball is reached when the gravitational force is balanced by the drag force. If the drag coefficient is 0.5 and the fluid has a viscosity of 0.1 Pa-s, what is the terminal velocity of the ball?a)0.5 m/sb)1.0 m/sc)1.5 m/sd)2.0 m/sCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
Download more important topics, notes, lectures and mock test series for Mechanical Engineering Exam by signing up for free.
Here you can find the meaning of A ball of radius 0.02 m falls under the influence of gravity through a viscous fluid. The terminal velocity of the ball is reached when the gravitational force is balanced by the drag force. If the drag coefficient is 0.5 and the fluid has a viscosity of 0.1 Pa-s, what is the terminal velocity of the ball?a)0.5 m/sb)1.0 m/sc)1.5 m/sd)2.0 m/sCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A ball of radius 0.02 m falls under the influence of gravity through a viscous fluid. The terminal velocity of the ball is reached when the gravitational force is balanced by the drag force. If the drag coefficient is 0.5 and the fluid has a viscosity of 0.1 Pa-s, what is the terminal velocity of the ball?a)0.5 m/sb)1.0 m/sc)1.5 m/sd)2.0 m/sCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for A ball of radius 0.02 m falls under the influence of gravity through a viscous fluid. The terminal velocity of the ball is reached when the gravitational force is balanced by the drag force. If the drag coefficient is 0.5 and the fluid has a viscosity of 0.1 Pa-s, what is the terminal velocity of the ball?a)0.5 m/sb)1.0 m/sc)1.5 m/sd)2.0 m/sCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of A ball of radius 0.02 m falls under the influence of gravity through a viscous fluid. The terminal velocity of the ball is reached when the gravitational force is balanced by the drag force. If the drag coefficient is 0.5 and the fluid has a viscosity of 0.1 Pa-s, what is the terminal velocity of the ball?a)0.5 m/sb)1.0 m/sc)1.5 m/sd)2.0 m/sCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A ball of radius 0.02 m falls under the influence of gravity through a viscous fluid. The terminal velocity of the ball is reached when the gravitational force is balanced by the drag force. If the drag coefficient is 0.5 and the fluid has a viscosity of 0.1 Pa-s, what is the terminal velocity of the ball?a)0.5 m/sb)1.0 m/sc)1.5 m/sd)2.0 m/sCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
|
|
Explore Courses for Mechanical Engineering exam
|
|
Signup to solve all Doubts
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up
within 7 days!
within 7 days!
Takes less than 10 seconds to signup