Question

obtain the expression for terminal velocity ?
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Answer 1

Answer:

Explanation:

# 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 gravit

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

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 U