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The velocity of a small ball of mass 'm' and density d1, when dropped in a container filled with glycerine, becomes constant after some time. If the density of glycerine is d2, then the viscous force acting on the ball will be
- mg(1 - d1/d2)
- mg(1 - d2/d1)
- mg(d1/d2 - 1)
- mg(d2/d1 - 1)
Correct answer: mg(1 - d2/d1)
Solution
The correct option reflects the balance of forces acting on the ball when it reaches terminal velocity. At this point, the upward viscous force equals the downward gravitational force, leading to the relationship where the viscous force is proportional to the difference in densities, specifically mg(1 - d2/d1), indicating how the buoyant force affects the ball's motion.
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