The velocity of a small ball of mass 'm' and density d₁, when dropped in a container filled with glycerin, becomes constant after some time. If the density of glycerin is d₂, then the viscous force acting on the ball, will be :

Solution

Physics sir · 3 steps

Constant velocity means zero net force, so weight equals buoyancy plus viscous drag.

1. Three forces. Once the ball moves at terminal velocity, three forces act on it. Weight mg acts down, while the buoyant force and the viscous force both act up.
2. Buoyant force. The ball's volume is V = m/d₁. The glycerin it pushes aside has mass V d₂, so the buoyant force is m/d₁ d₂ g = mgd₂/d₁.

   Fᵥ = mg - mgd₂/d₁ = mg(1 - d₂/d₁)

3. So. The viscous force is mg(1 - d₂/d₁), which is option (b). It is positive, as it should be, because the ball sinks only when d₁ > d₂.

The idea to keep. At terminal velocity, balance all the forces. Buoyancy is always the body's weight scaled by ρ_(fluid)/ρ_(body), which gives mgρ_(fluid)/ρ_(body).

Answer from the NTA final answer key. Solution by PrepWiser.