$A$ spherical body of radius $r$ and density $\sigma$ falls freely through a viscous liquid having density $\rho$ and viscosity $\eta$ and attains a terminal velocity $v_0$. The estimated maximum error in the quantity $\eta$ is: (Ignore errors associated with $\sigma, \rho$ and $g$,gravitational acceleration)

• A
  $2 \frac{\Delta r}{r} - \frac{\Delta v_0}{v_0}$
• B
  $2 \frac{\Delta r}{r} + \frac{\Delta v_0}{v_0}$
• C
  $2 \left[ \frac{\Delta r}{r} + \frac{\Delta v_0}{v_0} \right]$
• D
  $2 \left[ \frac{\Delta r}{r} - \frac{\Delta v_0}{v_0} \right]$