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6. The velocity of a small ball of mass M and density d, when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is 2 d , then the viscous force acting on the ball will be (1) 2Mg (2) 2 Mg (3) Mg (4) 3 2 Mg?
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6. The velocity of a small ball of mass M and density d, when dropped ...
Answer:
Concept: Viscous force acting on an object moving through a fluid is given by Stoke's law, which states that the force is proportional to the velocity of the object and the viscosity of the fluid.
Given:
- Mass of small ball = M
- Density of small ball = d
- Density of glycerine = 2d
- Velocity of small ball becomes constant after some time
To find: Viscous force acting on the ball
Solution:
1. Let's first find the buoyant force acting on the ball.
Buoyant force (Fb) = Weight of fluid displaced by the ball
= Volume of ball x Density of fluid x Acceleration due to gravity
= (4/3)πr³ x 2d x g [as density of glycerine = 2d]
= (8/3)πr³d g
2. Now, let's find the weight of the ball.
Weight of ball (Fw) = Mass of ball x Acceleration due to gravity
= Mg
3. Since the ball is moving at a constant velocity through the fluid, the viscous force (Fv) acting on the ball is equal and opposite to the sum of buoyant force and weight of the ball.
Fv = Fb + Fw
4. Substituting the values of Fb and Fw, we get
Fv = (8/3)πr³d g + Mg
5. Therefore, the viscous force acting on the ball is given by option (4) 3/2 Mg.
Final Answer: The viscous force acting on the ball is 3/2 Mg.
Concept: Viscous force acting on an object moving through a fluid is given by Stoke's law, which states that the force is proportional to the velocity of the object and the viscosity of the fluid.
Given:
- Mass of small ball = M
- Density of small ball = d
- Density of glycerine = 2d
- Velocity of small ball becomes constant after some time
To find: Viscous force acting on the ball
Solution:
1. Let's first find the buoyant force acting on the ball.
Buoyant force (Fb) = Weight of fluid displaced by the ball
= Volume of ball x Density of fluid x Acceleration due to gravity
= (4/3)πr³ x 2d x g [as density of glycerine = 2d]
= (8/3)πr³d g
2. Now, let's find the weight of the ball.
Weight of ball (Fw) = Mass of ball x Acceleration due to gravity
= Mg
3. Since the ball is moving at a constant velocity through the fluid, the viscous force (Fv) acting on the ball is equal and opposite to the sum of buoyant force and weight of the ball.
Fv = Fb + Fw
4. Substituting the values of Fb and Fw, we get
Fv = (8/3)πr³d g + Mg
5. Therefore, the viscous force acting on the ball is given by option (4) 3/2 Mg.
Final Answer: The viscous force acting on the ball is 3/2 Mg.
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6. The velocity of a small ball of mass M and density d, when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is 2 d , then the viscous force acting on the ball will be (1) 2Mg (2) 2 Mg (3) Mg (4) 3 2 Mg?
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6. The velocity of a small ball of mass M and density d, when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is 2 d , then the viscous force acting on the ball will be (1) 2Mg (2) 2 Mg (3) Mg (4) 3 2 Mg? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about 6. The velocity of a small ball of mass M and density d, when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is 2 d , then the viscous force acting on the ball will be (1) 2Mg (2) 2 Mg (3) Mg (4) 3 2 Mg? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 6. The velocity of a small ball of mass M and density d, when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is 2 d , then the viscous force acting on the ball will be (1) 2Mg (2) 2 Mg (3) Mg (4) 3 2 Mg?.
6. The velocity of a small ball of mass M and density d, when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is 2 d , then the viscous force acting on the ball will be (1) 2Mg (2) 2 Mg (3) Mg (4) 3 2 Mg? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about 6. The velocity of a small ball of mass M and density d, when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is 2 d , then the viscous force acting on the ball will be (1) 2Mg (2) 2 Mg (3) Mg (4) 3 2 Mg? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 6. The velocity of a small ball of mass M and density d, when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is 2 d , then the viscous force acting on the ball will be (1) 2Mg (2) 2 Mg (3) Mg (4) 3 2 Mg?.
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