Explain least count and least count error. Write a note on least count error.
(N/A) The smallest value that can be measured by a measuring instrument is called its least count.
- All readings or measured values are accurate only up to this value.
- The error associated with the resolution of the instrument is called the least count error.
- The least count of a vernier caliper is $0.01 \text{ cm}$,and the least count of a spherometer is $0.001 \text{ cm}$.
- Least count error belongs to the category of random errors but is limited in size.
- It can occur alongside both systematic and random errors.
- The least count of a standard meter scale is $1 \text{ mm}$.
- Least count error can be reduced by using instruments of higher precision and by improving experimental techniques.
- By repeating the observation several times and taking the arithmetic mean of all observations,the mean value becomes very close to the true value of the measured quantity.
- All readings or measured values are accurate only up to this value.
- The error associated with the resolution of the instrument is called the least count error.
- The least count of a vernier caliper is $0.01 \text{ cm}$,and the least count of a spherometer is $0.001 \text{ cm}$.
- Least count error belongs to the category of random errors but is limited in size.
- It can occur alongside both systematic and random errors.
- The least count of a standard meter scale is $1 \text{ mm}$.
- Least count error can be reduced by using instruments of higher precision and by improving experimental techniques.
- By repeating the observation several times and taking the arithmetic mean of all observations,the mean value becomes very close to the true value of the measured quantity.
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Similar Questions
$A$ student determined Young's Modulus of elasticity using the formula $Y = \frac{M g L^{3}}{4 b d^{3} \delta}$. The value of $g$ is taken to be $9.8 \, m/s^2$, without any significant error. His observations are as follows:
Physical Quantity Least count and Observed value Mass $(M)$ $1 \, g$ and $2 \, kg$ Length of bar $(L)$ $1 \, mm$ and $1 \, m$ Breadth of bar $(b)$ $0.1 \, mm$ and $4 \, cm$ Thickness of bar $(d)$ $0.01 \, mm$ and $0.4 \, cm$ Depression $(\delta)$ $0.01 \, mm$ and $5 \, mm$
Then the fractional error in the measurement of $Y$ is:
| Physical Quantity | Least count and Observed value |
| Mass $(M)$ | $1 \, g$ and $2 \, kg$ |
| Length of bar $(L)$ | $1 \, mm$ and $1 \, m$ |
| Breadth of bar $(b)$ | $0.1 \, mm$ and $4 \, cm$ |
| Thickness of bar $(d)$ | $0.01 \, mm$ and $0.4 \, cm$ |
| Depression $(\delta)$ | $0.01 \, mm$ and $5 \, mm$ |
Then the fractional error in the measurement of $Y$ is:
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