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Spherical balls of radius R are falling in a viscous fluid of viscosity η with a velocity v. The retarding viscous force acting on the spherical ball is
- a)directly proportional to R but inversely proportional to v
- b)directly proportional to both radius R and velocity v
- c)inversely proportional to both radius R and velocity v
- d)inversely proportional to R but directly proportional to velocity v
Correct answer is option 'B'. Can you explain this answer?
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Spherical balls of radius R are falling in a viscous fluid of viscosit...
Η. The velocity of each ball is given by the Stokes law:
v = (2/9) (ρs - ρf) g R^2 / η
where ρs is the density of the ball, ρf is the density of the fluid, g is the acceleration due to gravity, and η is the viscosity of the fluid.
This equation shows that the velocity of the ball is proportional to the radius of the ball squared, the difference in density between the ball and the fluid, and the acceleration due to gravity. It is also inversely proportional to the viscosity of the fluid.
Therefore, larger balls will fall faster than smaller balls, assuming all other factors are the same. Balls that are denser than the fluid will fall faster than less dense balls. A higher acceleration due to gravity will also cause the balls to fall faster.
However, the viscosity of the fluid will slow down the balls, making them fall at a slower rate. This is why very small particles, such as nanoparticles, can remain suspended in a fluid for a long time due to the high viscosity of the fluid.
Overall, the motion of falling spherical balls in a viscous fluid is complex and depends on several factors. The Stokes law provides a useful approximation for calculating the velocity of falling balls in a viscous fluid, but it is important to consider all the relevant factors to accurately predict the motion of the balls.
v = (2/9) (ρs - ρf) g R^2 / η
where ρs is the density of the ball, ρf is the density of the fluid, g is the acceleration due to gravity, and η is the viscosity of the fluid.
This equation shows that the velocity of the ball is proportional to the radius of the ball squared, the difference in density between the ball and the fluid, and the acceleration due to gravity. It is also inversely proportional to the viscosity of the fluid.
Therefore, larger balls will fall faster than smaller balls, assuming all other factors are the same. Balls that are denser than the fluid will fall faster than less dense balls. A higher acceleration due to gravity will also cause the balls to fall faster.
However, the viscosity of the fluid will slow down the balls, making them fall at a slower rate. This is why very small particles, such as nanoparticles, can remain suspended in a fluid for a long time due to the high viscosity of the fluid.
Overall, the motion of falling spherical balls in a viscous fluid is complex and depends on several factors. The Stokes law provides a useful approximation for calculating the velocity of falling balls in a viscous fluid, but it is important to consider all the relevant factors to accurately predict the motion of the balls.
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Spherical balls of radius R are falling in a viscous fluid of viscosity η with a velocity v. The retarding viscous force acting on the spherical ball isa)directly proportional to R but inversely proportional to vb)directly proportional to both radius R and velocity vc)inversely proportional to both radius R and velocity vd)inversely proportional to R but directly proportional to velocity vCorrect answer is option 'B'. Can you explain this answer?
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Spherical balls of radius R are falling in a viscous fluid of viscosity η with a velocity v. The retarding viscous force acting on the spherical ball isa)directly proportional to R but inversely proportional to vb)directly proportional to both radius R and velocity vc)inversely proportional to both radius R and velocity vd)inversely proportional to R but directly proportional to velocity vCorrect answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Spherical balls of radius R are falling in a viscous fluid of viscosity η with a velocity v. The retarding viscous force acting on the spherical ball isa)directly proportional to R but inversely proportional to vb)directly proportional to both radius R and velocity vc)inversely proportional to both radius R and velocity vd)inversely proportional to R but directly proportional to velocity vCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Spherical balls of radius R are falling in a viscous fluid of viscosity η with a velocity v. The retarding viscous force acting on the spherical ball isa)directly proportional to R but inversely proportional to vb)directly proportional to both radius R and velocity vc)inversely proportional to both radius R and velocity vd)inversely proportional to R but directly proportional to velocity vCorrect answer is option 'B'. Can you explain this answer?.
Spherical balls of radius R are falling in a viscous fluid of viscosity η with a velocity v. The retarding viscous force acting on the spherical ball isa)directly proportional to R but inversely proportional to vb)directly proportional to both radius R and velocity vc)inversely proportional to both radius R and velocity vd)inversely proportional to R but directly proportional to velocity vCorrect answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Spherical balls of radius R are falling in a viscous fluid of viscosity η with a velocity v. The retarding viscous force acting on the spherical ball isa)directly proportional to R but inversely proportional to vb)directly proportional to both radius R and velocity vc)inversely proportional to both radius R and velocity vd)inversely proportional to R but directly proportional to velocity vCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Spherical balls of radius R are falling in a viscous fluid of viscosity η with a velocity v. The retarding viscous force acting on the spherical ball isa)directly proportional to R but inversely proportional to vb)directly proportional to both radius R and velocity vc)inversely proportional to both radius R and velocity vd)inversely proportional to R but directly proportional to velocity vCorrect answer is option 'B'. Can you explain this answer?.
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