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Using dimensions show that the viscous force acting on a glass sphere falling through a highly viscous liquid of coefficient of viscosity eta is Fprop eta av where a is the radius of the sphere and v its terminal velocity.

Answer» <html><body><p></p>Solution :Dimensional formula of `eta` is `[ML^(-1)T^(-1)]` <br/> `F <a href="https://interviewquestions.tuteehub.com/tag/prop-607409" style="font-weight:bold;" target="_blank" title="Click to know more about PROP">PROP</a> eta^(x)a^(y)v^(z)` <br/> `F=keta^(x)a^(y)v^(z)`, k is dimensionaless constant <br/> Taking <a href="https://interviewquestions.tuteehub.com/tag/dimensions-439808" style="font-weight:bold;" target="_blank" title="Click to know more about DIMENSIONS">DIMENSIONS</a> on both <a href="https://interviewquestions.tuteehub.com/tag/sides-1207029" style="font-weight:bold;" target="_blank" title="Click to know more about SIDES">SIDES</a> <br/> `MLT^(-2)=[ML^(-1)T^(-1)]^(x)[<a href="https://interviewquestions.tuteehub.com/tag/l-535906" style="font-weight:bold;" target="_blank" title="Click to know more about L">L</a>]^(y)[LT^(-1)]^(z)` <br/> `MLT^(-2)=M^(x)L^(-1)T^(-x)L^(y)T^(-z)` <br/> `MLT^(-2)=M^(x)L^(-x+y+z)T^(x-x-z)` <br/> <a href="https://interviewquestions.tuteehub.com/tag/equating-7679226" style="font-weight:bold;" target="_blank" title="Click to know more about EQUATING">EQUATING</a> dimensions on both sides <br/> of M, `1=x""` i.e. x=1 <br/> of T `2=-x-z""-z=-2+x=-2+1,z=1` <br/> of L `1=-x+y+z=-1+y+1""` i.e. `y=1` <br/> `F=k eta^(1)a^(1)v^(1)` <br/> or `F prop eta av`.</body></html>


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