The terminal velocity of solid sphere of radius 0.1 m moving in air in vertically downward dire

step 1 In this problem, I can write the formula of terminal velocity is equal to 2 by 9, multiplication

The terminal velocity of solid sphere of radius 0.1 m...

The terminal velocity of solid sphere of radius $0.1 \mathrm{~m}$ moving in air in vertically downward direction, is: (\eta $=1.8 \times 10^{-5} \mathrm{Ns} / \mathrm{m}^{2}$, density of sphere $=1000 \mathrm{~kg} / \mathrm{m}^{3}$ and $\left.g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$ (a) $2 \times 10^{5} \mathrm{~m} / \mathrm{s}$ (b) $1.2 \times 10^{8} \mathrm{~cm} / \mathrm{s}$ (c) $4 \times 10^{2} \mathrm{~cm} / \mathrm{s}$ (d) none of these

The terminal velocity of solid sphere of radius $0.1 \mathrm{~m}$ moving in air in vertically downward direction, is:
(\eta $=1.8 \times 10^{-5} \mathrm{Ns} / \mathrm{m}^{2}$, density of sphere $=1000 \mathrm{~kg} / \mathrm{m}^{3}$ and
$\left.g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$
(a) $2 \times 10^{5} \mathrm{~m} / \mathrm{s}$
(b) $1.2 \times 10^{8} \mathrm{~cm} / \mathrm{s}$
(c) $4 \times 10^{2} \mathrm{~cm} / \mathrm{s}$
(d) none of these

Key Concepts

Terminal Velocity

Terminal velocity refers to the constant speed that a falling object reaches when the force of gravity is balanced by the drag (or resistance) force from the fluid through which it is moving. At this velocity, the net acceleration becomes zero because all the forces acting on the object are in equilibrium.

Drag Force

Drag force is the resistive force exerted by a fluid (such as air or water) that opposes the motion of an object moving through it. It generally depends on factors such as the object’s shape, size, velocity, and the properties of the fluid, and it may be modeled as either proportional to the velocity or the square of the velocity depending on the flow regime.

Force Equilibrium

In the context of terminal velocity, force equilibrium is the condition where the gravitational force acting on a moving object is exactly balanced by the drag force, leading to zero net force and, consequently, no further acceleration. This balance is key in determining terminal speed.

Stokes' Law

Stokes' law provides an expression for the drag force experienced by small spherical objects moving at low velocities in a viscous fluid, where the flow is laminar. It is crucial for analyzing situations where viscous forces dominate over inertial forces, although its applicability needs to be verified based on the object's size and the flow's Reynolds number.

Reynolds Number

The Reynolds number is a dimensionless quantity used in fluid dynamics to predict the flow regime around an object, indicating whether the flow is laminar or turbulent. It helps in determining the appropriate drag force model to use, such as whether to apply Stokes' law for low Reynolds numbers or a quadratic drag model for higher Reynolds numbers.

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