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CBSE Class 11-science Answered

the terminal velocity v of a spherical ball of lead of radius r falling through a viscous liquid varies with r such that
Asked by rupimadhes | 21 Nov, 2023, 05:31: AM
answered-by-expert Expert Answer
If the spherical ball reaches the terminal velocity v while falling though viscous liquid , then resistive viscous force F equals weight  Wl in liquid of the spherical ball
 
begin mathsize 14px style F space equals space W subscript l end style
begin mathsize 14px style 6 straight pi space r space straight eta space straight v space equals space V space left parenthesis space rho space minus space rho subscript l right parenthesis space space straight g end style  ............................. (1)
 
where r is radius of ball , η is viscosity of liquid , v is terminal speed , V is volume of ball , ρ is density of ball ,
ρl is density of liquid and acceleration due to gravity.
 
Volume V   begin mathsize 14px style equals space 4 over 3 straight pi space straight r cubed space end style  ........................(2)
By substituting mass V from eqn.(2) , we rewrite eqn.(1) as
 
begin mathsize 14px style 6 pi space r space eta space v space equals space 4 over 3 pi space r cubed space cross times left parenthesis space rho space minus space rho subscript l right parenthesis space cross times g end style
 
Hence terminal speed v is
 
 
begin mathsize 14px style v space equals space 2 over 9 space cross times fraction numerator left parenthesis space rho space minus space rho subscript l right parenthesis g over denominator eta end fraction cross times space r squared end style
 
hence terminal speed varies with square of radius
Answered by Thiyagarajan K | 21 Nov, 2023, 11:44: AM

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