A spherical body of radius r and density falls freely through a viscous liquid having density and viscosity and attains a terminal velocity v₀ . Estimated maximum error in the quantity is : (Ignore errors associated with , and g , gravitational acceleration)

Step-by-step solution

The terminal velocity v₀ of a spherical body falling through a viscous liquid is given by Stokes' Law: v₀ = 2r^2( - )g 9 Rearranging the formula to express viscosity in terms of other variables: = 2r^2( - )g 9v₀ Since we are told to ignore errors associated with , , and g , these quantities along with the numerical factor 2 9 are treated as constants. The expression for can be written as = k r^2 v₀ , where k = 2( - )g 9 is a constant. Taking the natural logarithm on both sides: = k + 2 r - v₀ Differentiating both s