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.
The relative error in the determination of the surface area of a sphere is $\alpha $. Then the relative error in the determination of its volume is
A person measures the depth of a well by measuring the time interval between dropping a stone and receiving the sound of impact with the bottom of the well. The error in his measurement of time is $\delta \mathrm{T}=0.01$ seconds and he measures the depth of the well to be $\mathrm{L}=20$ meters. Take the acceleration due to gravity $\mathrm{g}=10 \mathrm{~ms}^{-2}$ and the velocity of sound is $300 \mathrm{~ms}^{-1}$. Then the fractional error in the measurement, $\delta \mathrm{L} / \mathrm{L}$, is closest to
If error in measuring diameter of a circle is $4\%$, the error in radius of the circle would be
Two resistance are measured in $Ohm$ and is given as
$R_1 = 3 \Omega \pm 1\%$ and $R_2 = 6 \Omega \pm 2\%$ When they are connected in parallel, the percentage error in equivalent resistance is.......... $\%$
The density of a cube is measured by measuring its mass and length of its sides. If the maximum error in the measurement of mass and length are $4\%$ and $3\%$ respectively, the maximum error in the measurement of density will be ........ $\%$