Question

derive the expression for terminal velocity.( plz don't spam guys )☺️☺️❤️❤️❤️​

Answer 1

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Here is ur answer

STATEMENT:

# The maximum constant velocity acquired by a body while falling through a viscous medium is called its Terminal Velocity.

# It is attained when force of resistance of a medium is equal and opposite to the force of gravity.

DERIVATION:

Expression for terminal velocity,

V = Vt

Density of a sphere = ρ

Density of a viscous fluid = σ

Density of a sphere rolling on a viscous force = ( ρ - σ )

Volume of the sphere = 4 /3 πr³

Viscous force = mg

6πηrv = mg

6πηrv = ( d × v ) g

6πηrv = ( ρ - σ )4 /3 πr³

Here π and r will get cancelled out,

6ηv = ( ρ - σ )4 /3 r²g

v = ( ρ - σ )4 /3 r²g × 1 /6η

= ( ρ - σ ) 2r²/9η .g

Therefore,

V = 2r² ( ρ - σ ) g / 9η

Hope it helps

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Answer 2

Explanation:

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At some velocity v = vo, the resultant of all the forces acting on body reduces to zero and body acquires the constant velocity known as terminal velocity. The above expression represents the terminal velocity acquired by a spherical body falling in viscous media under gravity.

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