The velocity of a small ball of mass m and density d1 when dropped in a container filled with gl

step 1 According to this question we know that viscous force is equal to weight minus beyond force so w

The velocity of a small ball of mass m and density d1 when...

The velocity of a small ball of mass $\mathrm{m}$ and density $\mathrm{d}_{1}$ when dropped in a container filled with glycerine becomes constants after sometime. What is the viscous force acting on the ball ? (density of glycerine is $\mathrm{d}_{2}$ ) (A) $m g\left\{1-\left(d_{1} / d_{2}\right)\right\}$ (B) $m g\left\{1-\left(d_{2} / d_{1}\right)\right\}$ (C) $m g\left\{d_{1} /\left(d_{1}-d_{2}\right)\right\}$ (D) $\operatorname{mg}\left\{\mathrm{d}_{2} /\left(\mathrm{d}_{1}-\mathrm{d}_{2}\right)\right\}$

The velocity of a small ball of mass $\mathrm{m}$ and density $\mathrm{d}_{1}$ when dropped in a container filled with glycerine becomes constants after sometime. What is the viscous force acting on the ball ? (density of glycerine is $\mathrm{d}_{2}$ )
(A) $m g\left\{1-\left(d_{1} / d_{2}\right)\right\}$
(B) $m g\left\{1-\left(d_{2} / d_{1}\right)\right\}$
(C) $m g\left\{d_{1} /\left(d_{1}-d_{2}\right)\right\}$
(D) $\operatorname{mg}\left\{\mathrm{d}_{2} /\left(\mathrm{d}_{1}-\mathrm{d}_{2}\right)\right\}$

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Key Concepts

Terminal Velocity

Terminal velocity is achieved when an object moving through a fluid reaches a constant speed because the net forces acting on it cancel out. At this point, the driving forces (such as gravity) are balanced by the resistive forces (such as buoyant and viscous forces), resulting in zero acceleration.

Buoyant Force

Buoyant force is the upward force experienced by an object submerged in a fluid, equal to the weight of the displaced fluid. It effectively reduces the object's apparent weight in the fluid and is a crucial factor in determining the net force acting on the object.

Viscous Force (Drag Force)

Viscous force, often referred to as drag in this context, is the resistive force exerted by a fluid on an object moving through it. As the object accelerates, this force increases until it balances the net driving force (weight minus buoyant force), causing the object to move at a constant terminal velocity.

Force Equilibrium

Force equilibrium occurs when all the forces acting on an object cancel each other out, resulting in no net force. In the context of an object submerged in a viscous fluid, reaching force equilibrium means that the upward viscous and buoyant forces exactly balance the downward gravitational force.

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