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
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](https://images.topperlearning.com/topper/tinymce/cache/630f0e989ed6a367d7a0e429ba6c6d97.png)
![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](https://images.topperlearning.com/topper/tinymce/cache/bbf408c04b2591095e740349975e91a2.png)
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
........................(2)
![begin mathsize 14px style equals space 4 over 3 straight pi space straight r cubed space end style](https://images.topperlearning.com/topper/tinymce/cache/b7bd7c8dbd6a5dcda9d0dbcdf433a033.png)
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](https://images.topperlearning.com/topper/tinymce/cache/5e9c990ee80cc99923236b38cbe8b4cf.png)
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](https://images.topperlearning.com/topper/tinymce/cache/c660cf5e2fcb5e04f3f9d4a970487b2d.png)
hence terminal speed varies with square of radius
Answered by Thiyagarajan K | 21 Nov, 2023, 11:44: AM
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