A spherical body of radius 
and density 
falls freely through a viscous liquid having density 
and viscosity 
and attains a terminal velocity 
. Estimated maximum error in the quantity 
is : (Ignore errors associated with 
and 
, gravitational acceleration)
Text Solution
Verified by ExpertsA
The terminal velocity 
of a spherical body falling through a viscous liquid is given by Stokes' Law:
Rearranging the formula to express viscosity 
in terms of other variables:
Since we are told to ignore errors associated with 
, and 
, these quantities along with the numerical factor 
are treated as constants.
The expression for 
can be written as 
, where 
is a constant.
Taking the natural logarithm on both sides:
Differentiating both sides to find the relative error:
For the estimated maximum fractional error, we take the absolute sum of the individual relative errors:
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