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

Options

A. Pressure difference
B. Volume of the liquid collected
C. Length of the capillary tube
D. Inner radius of the capillary tube

Answer

To determine the physical quantity that requires greater accuracy in measurement in Poiseuille's method of determining the coefficient of viscosity, we can follow these steps:

### Step 1: Understand Poiseuille's Law
Poiseuille's law states that the coefficient of viscosity (η) can be calculated using the formula:
\[ \eta = \frac{\pi P R^4}{8 V L} \]
where:
- \( P \) = pressure difference
- \( R \) = radius of the capillary tube
- \( V \) = rate of flow
- \( L \) = length of the capillary tube

### Step 2: Identify the Variables
In the formula, we have four variables: pressure difference (\( P \)), radius of the capillary tube (\( R \)), rate of flow (\( V \)), and length of the capillary tube (\( L \)). Each of these variables contributes to the calculation of viscosity.

### Step 3: Analyze the Sensitivity of Each Variable
To determine which variable requires the most accuracy, we can analyze how errors in measurement of each variable affect the calculation of viscosity.

1. **Pressure Difference (\( P \))**: An error in pressure measurement can affect the result, but the impact is relatively moderate.
2. **Radius of the Capillary Tube (\( R \))**: Since \( R \) is raised to the fourth power in the equation, any small error in measuring \( R \) will have a significant impact on the calculated viscosity.
3. **Rate of Flow (\( V \))**: An error in flow rate affects the result, but again, the impact is less severe than that of \( R \).
4. **Length of the Capillary Tube (\( L \))**: Errors in measuring \( L \) will also affect the viscosity calculation, but not as critically as \( R \).

### Step 4: Conclusion
Given that the radius \( R \) is raised to the fourth power, it is the physical quantity that requires the greatest accuracy in measurement in Poiseuille's method. Therefore, the answer to the question is:

**The radius of the capillary tube (R) requires greater accuracy in measurement.**

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