In Poiseuilli's method of determination of coefficient of viscosity, the physical quantity that requires greater accuracy in measurement is

The correct answer is Inner radius of the capillary tube.

Explanation:

According to Poiseuille's formula, the volume of liquid flowing per second through a capillary tube of length l and radius r under a pressure difference P is given by:

$V=\frac{\pi P{r}^4}{8\eta l}$

Rearranging the formula to solve for the coefficient of viscosity ($\eta$), we get:

$\eta =\frac{\pi P{r}^4}{8Vl}$

To analyze the maximum fractional error or percentage error in measuring $\eta$, we take the logarithmic differential of the equation:

$\frac{\Delta \eta }{\eta }=\frac{\Delta P}{P}+4\left(\frac{\Delta r}{r}\right)+\frac{\Delta V}{V}+\frac{\Delta l}{l}$

From the above relation, we can see that the fractional error in the radius ($r$) is multiplied by a factor of 4. Therefore, any small error or uncertainty in measuring the inner radius ($r$) causes a fourfold increase in the percentage error of the coefficient of viscosity.

Hence, the inner radius of the capillary tube is the physical quantity that requires the greatest accuracy in measurement.