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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 d/2, then the viscous force acting on the ball will be :
- a)Mg/2
- b)Mg
- c)3/2 Mg
- d)2 Mg
Correct answer is option 'A'. Can you explain this answer?
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The velocity of a small ball of mass M and density d, when dropped in ...
Question Analysis:
We have a small ball of mass M and density d, which is dropped in a container filled with glycerine. After some time, the velocity of the ball becomes constant. We need to determine the viscous force acting on the ball. The density of glycerine is given as d/2.
Answer Explanation:
To solve this problem, we can use the concept of buoyancy and viscous force acting on the ball.
Buoyancy:
When an object is submerged in a fluid, it experiences an upward buoyant force equal to the weight of the fluid displaced by the object. This buoyant force can be calculated using the formula:
Buoyant force = density of fluid * volume of fluid displaced * acceleration due to gravity
In this case, the ball is submerged in glycerine, so the buoyant force acting on the ball is:
Buoyant force = (d/2) * volume of glycerine displaced * g
Viscous Force:
The viscous force acting on an object moving through a fluid is proportional to the velocity of the object and the viscosity of the fluid. Mathematically, it can be represented as:
Viscous force = coefficient of viscosity * velocity
In this case, the ball is moving through glycerine, so the viscous force acting on the ball is:
Viscous force = coefficient of viscosity * velocity
Equilibrium Condition:
According to the question, the velocity of the ball becomes constant after some time. This means that the buoyant force and the viscous force acting on the ball must be equal and opposite to each other for the ball to reach a constant velocity.
Therefore, we can equate the buoyant force and the viscous force:
(d/2) * volume of glycerine displaced * g = coefficient of viscosity * velocity
Conclusion:
From the equation above, we can see that the viscous force acting on the ball is directly proportional to the density of glycerine, which is d/2. Hence, the correct answer is option A: Mg/2.
We have a small ball of mass M and density d, which is dropped in a container filled with glycerine. After some time, the velocity of the ball becomes constant. We need to determine the viscous force acting on the ball. The density of glycerine is given as d/2.
Answer Explanation:
To solve this problem, we can use the concept of buoyancy and viscous force acting on the ball.
Buoyancy:
When an object is submerged in a fluid, it experiences an upward buoyant force equal to the weight of the fluid displaced by the object. This buoyant force can be calculated using the formula:
Buoyant force = density of fluid * volume of fluid displaced * acceleration due to gravity
In this case, the ball is submerged in glycerine, so the buoyant force acting on the ball is:
Buoyant force = (d/2) * volume of glycerine displaced * g
Viscous Force:
The viscous force acting on an object moving through a fluid is proportional to the velocity of the object and the viscosity of the fluid. Mathematically, it can be represented as:
Viscous force = coefficient of viscosity * velocity
In this case, the ball is moving through glycerine, so the viscous force acting on the ball is:
Viscous force = coefficient of viscosity * velocity
Equilibrium Condition:
According to the question, the velocity of the ball becomes constant after some time. This means that the buoyant force and the viscous force acting on the ball must be equal and opposite to each other for the ball to reach a constant velocity.
Therefore, we can equate the buoyant force and the viscous force:
(d/2) * volume of glycerine displaced * g = coefficient of viscosity * velocity
Conclusion:
From the equation above, we can see that the viscous force acting on the ball is directly proportional to the density of glycerine, which is d/2. Hence, the correct answer is option A: Mg/2.
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Community Answer
The velocity of a small ball of mass M and density d, when dropped in ...
Fr + Fb = Mg
Fr = Mg- Fb
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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 d/2, then the viscous force acting on the ball will be :a)Mg/2b)Mgc)3/2 Mgd)2 MgCorrect answer is option 'A'. Can you explain this answer?
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