Explain least count and least count error. Write a note on least count error.
The smallest value that can be measured by the measuring instrument is called its least count.
- All the readings or measured values are good only up to this value.
- Error associated with resolution of the instrument is called least count error.
- Least count of vernier is $0.01 \mathrm{~cm}$ and least count of spherometer is $0.001 \mathrm{~cm}$.
- Least count error belong to category of random error but within a limited size.
- It occur with both systematic and random error.
- Least count of meter scale is $1 \mathrm{~mm}$.
- Using instrument of higher precision, improving experimental technique we can reduce least count error.
Repeating the observation several times and taking arithmetic mean of all observation the mean value would be very close to the true value of the measured quantity.
A student performs an experiment to determine the Young's modulus of a wire, exactly $2 \mathrm{~m}$ long, by Searle's method. In a particular reading, the student measures the extension in the length of the wire to be $0.8 \mathrm{~mm}$ with an uncertainty of $\pm 0.05 \mathrm{~mm}$ at a load of exactly $1.0 \mathrm{~kg}$. The student also measures the diameter of the wire to be $0.4 \mathrm{~mm}$ with an uncertainty of $\pm 0.01 \mathrm{~mm}$. Take $g=9.8 \mathrm{~m} / \mathrm{s}^2$ (exact). The Young's modulus obtained from the reading is
Out of absolute error, relative error and fractional error which has unit and which has no unit ?
A public park, in the form of a square, has an area of $(100 \pm 0.2)\; m ^2$. The side of park is ............ $m$
The radius of a sphere is measured to be $(7.50 \pm 0.85) \,cm .$ Suppose the percentage error in its volume is $x$. The value of $x$, to the nearest integer is .....$\%$
The percentage error in measurement of a physical quantity $m$ given by $m = \pi \tan \theta $ is minimum when $\theta $ $=$ .......... $^o$ (Assume that error in $\theta $ remain constant)