If the terminal speed of a sphere of gold (density = 19.5 kgm^-3 ) is 0.2 ms^-1 in a viscous li

step 1 know that the terminal velocity in a in a viscous liquid is given by vt equal to 2 by 9 2 by 9 r

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

If the terminal speed of a sphere of gold (density = $19.5 \mathrm{kgm}^{-3}$ ) is $0.2 \mathrm{~ms}^{-1}$ in a viscous liquid (density $=$ $1.5 \mathrm{kgm}^{-3}$ ), 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. [2006] (A) $0.4 \mathrm{~ms}^{-1}$ (B) $0.133 \mathrm{~ms}^{-1}$ (C) $0.1 \mathrm{~ms}^{-1}$ (D) $0.2 \mathrm{~ms}^{-1}$

If the terminal speed of a sphere of gold (density = $19.5 \mathrm{kgm}^{-3}$ ) is $0.2 \mathrm{~ms}^{-1}$ in a viscous liquid (density $=$ $1.5 \mathrm{kgm}^{-3}$ ), 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. [2006]
(A) $0.4 \mathrm{~ms}^{-1}$
(B) $0.133 \mathrm{~ms}^{-1}$
(C) $0.1 \mathrm{~ms}^{-1}$
(D) $0.2 \mathrm{~ms}^{-1}$

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Key Concepts

Terminal Velocity

Terminal velocity is the constant speed reached by an object when the net force acting on it becomes zero. This occurs when the drag force from the fluid equals the net gravitational force acting on the body, and it is an essential concept in fluid dynamics for understanding motion through viscous media.

Stokes' Law

Stokes' law describes the drag force experienced by spherical objects moving through a viscous fluid at low Reynolds numbers. It relates the drag force to the object's radius, the fluid's viscosity, and the object's speed, providing a basis for determining the terminal velocity of small spheres in viscous liquids.

Density Difference and Buoyancy

The terminal velocity of an object in a fluid depends on the difference between its density and the density of the fluid. This density difference determines the net gravitational or buoyant force acting on the object, influencing its acceleration and ultimate constant speed in the fluid.

Viscous Drag

Viscous drag is the resistance force exerted by a fluid on an object moving through it. In the context of terminal velocity, viscous drag increases with speed until it balances the driving forces, resulting in a steady, constant velocity. This concept is critical for analyzing motion in fluids where viscosity plays a significant role.

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