The length, breadth and thickness of a block are measured as 125.5 cm, 5.0 cm and 0.32 cm respectively. Which one of the following measurements is most accurate

To determine which of the given measurements is the most accurate, we need to analyze the concepts of accuracy and precision in measurement.

The accuracy of a measurement is related to its fractional error or percentage error. A measurement with a smaller fractional error is considered to be more accurate (or having higher relative accuracy) because the uncertainty is a smaller fraction of the total measured value.
The fractional error is given by the formula:
$\text{Fractional Error}=\frac{\Delta x}{x}$
where $\Delta x$ represents the absolute error (the least count of the measuring instrument used) and $x$ is the measured value.

Let us calculate the fractional error for each measurement:

1. For Length:
Measured value, $L=125.5\text{cm}$
The measurement is recorded to one decimal place, so the least count (absolute error) is $\Delta L=0.1\text{cm}$.
The fractional error for length is:
$\frac{\Delta L}{L}=\frac{0.1}{125.5}\approx 0.000797$

2. For Breadth:
Measured value, $B=5.0\text{cm}$
The measurement is recorded to one decimal place, so the least count (absolute error) is $\Delta B=0.1\text{cm}$.
The fractional error for breadth is:
$\frac{\Delta B}{B}=\frac{0.1}{5.0}=0.02$

3. For Thickness:
Measured value, $T=0.32\text{cm}$
The measurement is recorded to two decimal places, so the least count (absolute error) is $\Delta T=0.01\text{cm}$.
The fractional error for thickness is:
$\frac{\Delta T}{T}=\frac{0.01}{0.32}=0.03125$

Comparing the fractional errors:
- Fractional error of length $\approx 0.0008$
- Fractional error of breadth $=0.02$
- Fractional error of thickness $\approx 0.031$

Since the fractional error is least for the measurement of length, the measurement of length is the most accurate.

Therefore, the correct option is Length.