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Two spheres of the same material, but of radii R and 3R are allowed to fall vertically downwards through a liquid of density σ. The ratio of their terminal velocities is
- a)1 : 3
- b)1 : 6
- c)1 : 9
- d)1 : 1
Correct answer is option 'C'. Can you explain this answer?
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Let's assume the density of the liquid is ρ.
When a sphere falls through a liquid, it experiences two forces: the gravitational force and the buoyant force.
The gravitational force acting on a sphere is given by the equation:
F_gravity = (4/3)πR^3ρg
where g is the acceleration due to gravity.
The buoyant force acting on a sphere is given by the equation:
F_buoyant = (4/3)πR^3ρ_lg
where ρ_l is the density of the liquid.
Since both spheres are made of the same material, their densities are the same. Therefore, the gravitational forces acting on both spheres are equal.
F_gravity1 = F_gravity2
(4/3)πR^3ρg = (4/3)π(3R)^3ρg
R^3ρg = (27R^3)ρg
R^3 = 27R^3
R = 3R
This means that the radius of the smaller sphere is one-third of the radius of the larger sphere.
In other words, the radius of the smaller sphere is R, and the radius of the larger sphere is 3R.
When a sphere falls through a liquid, it experiences two forces: the gravitational force and the buoyant force.
The gravitational force acting on a sphere is given by the equation:
F_gravity = (4/3)πR^3ρg
where g is the acceleration due to gravity.
The buoyant force acting on a sphere is given by the equation:
F_buoyant = (4/3)πR^3ρ_lg
where ρ_l is the density of the liquid.
Since both spheres are made of the same material, their densities are the same. Therefore, the gravitational forces acting on both spheres are equal.
F_gravity1 = F_gravity2
(4/3)πR^3ρg = (4/3)π(3R)^3ρg
R^3ρg = (27R^3)ρg
R^3 = 27R^3
R = 3R
This means that the radius of the smaller sphere is one-third of the radius of the larger sphere.
In other words, the radius of the smaller sphere is R, and the radius of the larger sphere is 3R.
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Two spheres of the same material, but of radii R and 3R are allowed to fall vertically downwards through a liquid of density σ. The ratio of their terminal velocities isa)1 : 3b)1 : 6c)1 : 9d)1 : 1Correct answer is option 'C'. Can you explain this answer?
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Two spheres of the same material, but of radii R and 3R are allowed to fall vertically downwards through a liquid of density σ. The ratio of their terminal velocities isa)1 : 3b)1 : 6c)1 : 9d)1 : 1Correct answer is option 'C'. 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 Two spheres of the same material, but of radii R and 3R are allowed to fall vertically downwards through a liquid of density σ. The ratio of their terminal velocities isa)1 : 3b)1 : 6c)1 : 9d)1 : 1Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two spheres of the same material, but of radii R and 3R are allowed to fall vertically downwards through a liquid of density σ. The ratio of their terminal velocities isa)1 : 3b)1 : 6c)1 : 9d)1 : 1Correct answer is option 'C'. Can you explain this answer?.
Two spheres of the same material, but of radii R and 3R are allowed to fall vertically downwards through a liquid of density σ. The ratio of their terminal velocities isa)1 : 3b)1 : 6c)1 : 9d)1 : 1Correct answer is option 'C'. 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 Two spheres of the same material, but of radii R and 3R are allowed to fall vertically downwards through a liquid of density σ. The ratio of their terminal velocities isa)1 : 3b)1 : 6c)1 : 9d)1 : 1Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two spheres of the same material, but of radii R and 3R are allowed to fall vertically downwards through a liquid of density σ. The ratio of their terminal velocities isa)1 : 3b)1 : 6c)1 : 9d)1 : 1Correct answer is option 'C'. Can you explain this answer?.
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