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Derive the expression of terminal velocity. |
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Answer» Hi 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 U |
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