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A small spherical ball of diameter 5mm is thrown into a well of water and it moves with a terminal velocity 10cm/s. Calculate the density of the spherical ball. Given that viscosity of water is 0.01poise.
- a)1.0083 gm/cm3
- b)1.0000 gm/cm3
- c)1.0023 gm/cm3
- d)1.0073 gm/cm3
Correct answer is option 'D'. Can you explain this answer?
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A small spherical ball of diameter 5mm is thrown into a well of water...
According to Stoke’s theorem,
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A small spherical ball of diameter 5mm is thrown into a well of water...
To calculate the density of the spherical ball, we need to use the concept of terminal velocity and the drag force acting on the ball.
1. Terminal Velocity:
Terminal velocity is the constant velocity reached by a falling object when the drag force equals the gravitational force acting on the object. It occurs when the net force on the object becomes zero.
2. Drag Force:
The drag force acting on an object moving through a fluid is given by the equation:
F_drag = 6πηrv
where F_drag is the drag force, η is the viscosity of the fluid, r is the radius of the ball, and v is the velocity of the ball.
3. Gravitational Force:
The gravitational force acting on the ball is given by:
F_gravity = ρVg
where F_gravity is the gravitational force, ρ is the density of the ball, V is the volume of the ball, and g is the acceleration due to gravity.
4. Equating Forces:
At terminal velocity, the drag force equals the gravitational force. Therefore, we can equate the two equations above:
6πηrv = ρVg
5. Diameter to Radius Conversion:
Given that the diameter of the ball is 5mm, we can calculate the radius as:
r = 0.5 * diameter = 0.5 * 5mm = 2.5mm = 0.25cm
6. Substituting Values:
Substituting the given values into the equation from step 4, we get:
6π * 0.01 * 0.25 * 10 = ρ * (4/3)π * (0.25)^3 * 9.8
7. Simplifying the Equation:
Simplifying the equation, we get:
1.5 = ρ * 0.065
8. Solving for Density:
Solving for density, we find:
ρ = 1.5 / 0.065 ≈ 23.077 gm/cm3
Since the options provided are in gm/cm3, we need to convert the density to the appropriate units:
ρ ≈ 1.0077 gm/cm3
Therefore, the correct answer is option D: 1.0073 gm/cm3.
1. Terminal Velocity:
Terminal velocity is the constant velocity reached by a falling object when the drag force equals the gravitational force acting on the object. It occurs when the net force on the object becomes zero.
2. Drag Force:
The drag force acting on an object moving through a fluid is given by the equation:
F_drag = 6πηrv
where F_drag is the drag force, η is the viscosity of the fluid, r is the radius of the ball, and v is the velocity of the ball.
3. Gravitational Force:
The gravitational force acting on the ball is given by:
F_gravity = ρVg
where F_gravity is the gravitational force, ρ is the density of the ball, V is the volume of the ball, and g is the acceleration due to gravity.
4. Equating Forces:
At terminal velocity, the drag force equals the gravitational force. Therefore, we can equate the two equations above:
6πηrv = ρVg
5. Diameter to Radius Conversion:
Given that the diameter of the ball is 5mm, we can calculate the radius as:
r = 0.5 * diameter = 0.5 * 5mm = 2.5mm = 0.25cm
6. Substituting Values:
Substituting the given values into the equation from step 4, we get:
6π * 0.01 * 0.25 * 10 = ρ * (4/3)π * (0.25)^3 * 9.8
7. Simplifying the Equation:
Simplifying the equation, we get:
1.5 = ρ * 0.065
8. Solving for Density:
Solving for density, we find:
ρ = 1.5 / 0.065 ≈ 23.077 gm/cm3
Since the options provided are in gm/cm3, we need to convert the density to the appropriate units:
ρ ≈ 1.0077 gm/cm3
Therefore, the correct answer is option D: 1.0073 gm/cm3.
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A small spherical ball of diameter 5mm is thrown into a well of water and it moves with a terminal velocity 10cm/s. Calculate the density of the spherical ball. Given that viscosity of water is 0.01poise.a)1.0083 gm/cm3b)1.0000 gm/cm3c)1.0023 gm/cm3d)1.0073 gm/cm3Correct answer is option 'D'. Can you explain this answer?
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A small spherical ball of diameter 5mm is thrown into a well of water and it moves with a terminal velocity 10cm/s. Calculate the density of the spherical ball. Given that viscosity of water is 0.01poise.a)1.0083 gm/cm3b)1.0000 gm/cm3c)1.0023 gm/cm3d)1.0073 gm/cm3Correct answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A small spherical ball of diameter 5mm is thrown into a well of water and it moves with a terminal velocity 10cm/s. Calculate the density of the spherical ball. Given that viscosity of water is 0.01poise.a)1.0083 gm/cm3b)1.0000 gm/cm3c)1.0023 gm/cm3d)1.0073 gm/cm3Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A small spherical ball of diameter 5mm is thrown into a well of water and it moves with a terminal velocity 10cm/s. Calculate the density of the spherical ball. Given that viscosity of water is 0.01poise.a)1.0083 gm/cm3b)1.0000 gm/cm3c)1.0023 gm/cm3d)1.0073 gm/cm3Correct answer is option 'D'. Can you explain this answer?.
A small spherical ball of diameter 5mm is thrown into a well of water and it moves with a terminal velocity 10cm/s. Calculate the density of the spherical ball. Given that viscosity of water is 0.01poise.a)1.0083 gm/cm3b)1.0000 gm/cm3c)1.0023 gm/cm3d)1.0073 gm/cm3Correct answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A small spherical ball of diameter 5mm is thrown into a well of water and it moves with a terminal velocity 10cm/s. Calculate the density of the spherical ball. Given that viscosity of water is 0.01poise.a)1.0083 gm/cm3b)1.0000 gm/cm3c)1.0023 gm/cm3d)1.0073 gm/cm3Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A small spherical ball of diameter 5mm is thrown into a well of water and it moves with a terminal velocity 10cm/s. Calculate the density of the spherical ball. Given that viscosity of water is 0.01poise.a)1.0083 gm/cm3b)1.0000 gm/cm3c)1.0023 gm/cm3d)1.0073 gm/cm3Correct answer is option 'D'. Can you explain this answer?.
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ample number of questions to practice A small spherical ball of diameter 5mm is thrown into a well of water and it moves with a terminal velocity 10cm/s. Calculate the density of the spherical ball. Given that viscosity of water is 0.01poise.a)1.0083 gm/cm3b)1.0000 gm/cm3c)1.0023 gm/cm3d)1.0073 gm/cm3Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice GATE tests.
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