A steel ball of diameter 3.2 mm falls under gravity through an oil of density 920 kg m^-3 and

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A steel ball of diameter 3.2 mm falls under gravity through...

A steel ball of diameter $3.2 \mathrm{~mm}$ falls under gravity through an oil of density $920 \mathrm{~kg} \mathrm{~m}^{-3}$ and viscosity $1.64 \mathrm{Ns} \mathrm{m}^{-2}$. The density of steel. may be taken as $7820 \mathrm{~kg} \mathrm{~m}^{-3}$. What is the terminal velocity of the ball ? (A) $3.45 \mathrm{cms}^{-1}$ (B) $4.25 \mathrm{cms}^{-1}$ (C) $1.85 \mathrm{~cm}^{-1}$ (D) $2.39 \mathrm{cms}^{-1}$

A steel ball of diameter $3.2 \mathrm{~mm}$ falls under gravity through an oil of density $920 \mathrm{~kg} \mathrm{~m}^{-3}$ and viscosity $1.64 \mathrm{Ns} \mathrm{m}^{-2}$. The density of steel. may be taken as $7820 \mathrm{~kg} \mathrm{~m}^{-3}$. What is the terminal velocity of the ball ?
(A) $3.45 \mathrm{cms}^{-1}$
(B) $4.25 \mathrm{cms}^{-1}$
(C) $1.85 \mathrm{~cm}^{-1}$
(D) $2.39 \mathrm{cms}^{-1}$

Key Concepts

Viscosity

Viscosity is a measure of a fluid's resistance to deformation or flow. It plays a critical role in determining how an object moves through a fluid because it influences the magnitude of the drag force experienced by the object. A higher viscosity means greater resistance, which in turn affects the terminal velocity of falling objects.

Buoyancy

Buoyancy is the upward force exerted by a fluid that opposes the weight of an immersed object. This force is determined by the volume of the displaced fluid and the fluid's density. In problems involving objects in fluids, buoyancy must be considered alongside gravitational and drag forces in order to determine the net force on the object.

Terminal Velocity

Terminal velocity is the constant speed attained by an object falling through a fluid when the net force acting on it becomes zero. At this point, the gravitational pull is exactly balanced by the resistive forces (such as drag and buoyancy), meaning the object no longer accelerates.

Stokes' Law

Stokes' Law provides a method to calculate the drag force experienced by spherical objects moving slowly through a viscous fluid. This law is applicable under laminar flow conditions and relates the drag force to the fluid’s viscosity, the object’s radius, and its velocity, making it essential for computing terminal speeds in viscous environments.

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