If the terminal speed of a sphere of gold (density =19.5 kg / m^3 ) is 0.2 m / s in a viscous l

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If the terminal speed of a sphere of gold (density =19.5 kg...

If the terminal speed of a sphere of gold (density $=19.5$ $\mathrm{kg} / \mathrm{m}^{3}$ ) is $0.2 \mathrm{~m} / \mathrm{s}$ in a viscous liquid $\left(\right.$ density $\left.=1.5 \mathrm{~kg} / \mathrm{m}^{3}\right)$ find the terminal speed of a sphere of silver (density = $10.5 \mathrm{~kg} / \mathrm{m}^{3}$ ) of the same size in the same liquid (a) $0.2 \mathrm{~m} / \mathrm{s}$ (b) $0.4 \mathrm{~m} / \mathrm{s}$ (c) $0.133 \mathrm{~m} / \mathrm{s}$ (d) $0.1 \mathrm{~m} / \mathrm{s}$

If the terminal speed of a sphere of gold (density $=19.5$ $\mathrm{kg} / \mathrm{m}^{3}$ ) is $0.2 \mathrm{~m} / \mathrm{s}$ in a viscous liquid $\left(\right.$ density $\left.=1.5 \mathrm{~kg} / \mathrm{m}^{3}\right)$
find the terminal speed of a sphere of silver (density = $10.5 \mathrm{~kg} / \mathrm{m}^{3}$ ) of the same size in the same liquid
(a) $0.2 \mathrm{~m} / \mathrm{s}$
(b) $0.4 \mathrm{~m} / \mathrm{s}$
(c) $0.133 \mathrm{~m} / \mathrm{s}$
(d) $0.1 \mathrm{~m} / \mathrm{s}$

Key Concepts

Density Difference

The density difference between an object and the fluid determines the net driving force acting on the object; it is the difference between the object’s density and the fluid’s density that dictates the effective weight or buoyancy. This concept is vital for understanding how different materials behave when moving through a fluid.

Viscous Drag

Viscous drag is the resistive force due to the viscosity of a fluid that opposes the motion of an object moving through it. This force increases with the object's speed and is essential for establishing terminal velocity by balancing the net gravitational force.

Stokes' Law

Stokes' law provides an expression for the drag force experienced by small, spherical objects moving at low speeds through a viscous fluid. It relates the drag force to the object's radius, its velocity, and the fluid's viscosity, thereby serving as a basis for calculating terminal velocity in such conditions.

Terminal Velocity

Terminal velocity is the constant speed attained by an object falling through a fluid when the net forces acting on it balance out. At this speed, the downward gravitational force is exactly balanced by the upward buoyant force and the viscous drag, resulting in zero net acceleration.

Buoyant Force

Buoyant force is the upward force exerted by a fluid on an immersed object, equal to the weight of the displaced fluid. This force opposes gravity and plays a crucial role in determining the net force acting on the object when it moves through a fluid.

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