Errors in Measurement

 The least count of a wrist watch graduated at every second is

Find percentage error in $Z$ if $Z= \frac{a^2{b}^{{\displaystyle \raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}}{\sqrt{c}{d}^{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}}$ and error in measuring $a,b,c,d$ are $2\%,1.5\%,4\%,2.5\%$.

How to calculate error when resistors are connected parallelly?

The pressure on a square plate is calculated by measuring the force on the plate and the length of the sides of the plate. If the maximum error in the measurement of force and length are $4\%$ and $2\%$, respectively, then the maximum error in the measurement of pressure is

Find the average absolute error in the following readings of period of oscillation of a simple pendulum: $2.63 \mathrm{s}, 2.56 \mathrm{s}, 2.42 \mathrm{s}, 2.71 \mathrm{s}$ and $2.80 \mathrm{s}$.

Explain the zero error. How it can be minimised?

The zero error is classified as:

When zero error is present in an instrument we get a reading when there should be no reading.

End correction is a correction in : 

The end correction is :

In acoustics, end correction is a short distance applied or added to the actual length of a resonance pipe, in order to calculate the precise resonant frequency of the pipe.

What is end correction?

The temperature today in Chicago is $50°F$. Instead of using the standard conversion formula ${}^{\circ }\mathrm{C}=\frac{5}{9}\times \left({}^{\circ }\mathrm{F}-32\right)$, Tommaso uses his grandmother's rule, which is easier but gives an approximate value: "Subtract $32$ from the value in $°F$ and multiply the result by $0.5$.

Calculate the actual and an approximate temperature in $°C$, using the standard formula and Tommaso's grandmother's rule. Calculate the percentage error of the approximate temperature value in $°C$.

The temperature today in Chicago is $50°F$. Instead of using the standard conversion formula ${}^{\circ }\mathrm{C}=\frac{5}{9}\times \left({}^{\circ }\mathrm{F}-32\right)$, Tommaso uses his grandmother's rule, which is easier but gives an approximate value: "Subtract $32$ from the value in $°F$ and multiply the result by $0.5$.

Calculate the actual and an approximate temperature in $°C$, using the standard formula and Tommaso's grandmother's rule.

Eratosthenes estimated the circumference of the Earth as $250000$ stadia (the length of an athletic stadium). If we assume he used the most common length of stadia of his time, his estimate of the circumference of the Earth would be $46620km$. Currently, the accepted average circumference of the Earth is $40030.2km$. Find the percentage error of Eratosthenes' estimate of the circumference of the Earth.

In $1856$, Andrew Waugh announced Mount Everest to be $8840m$ high, after several years of calculations based on observations made by the Great Trigonometric Survey. More recent surveys confirm the height as $8848m$. Calculate the percentage error made in the earlier survey.

Find the percentage error in using $3.14$ instead of $\mathrm{\pi }$.

For parallel resistors in an electrical circuit, the total resistance R is given by the formula, $\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}$. $R_1=7.2 Ohm$, measured to the nearest tenth and $R_2=3.6 Ohm$, also measured to the nearest tenth.

If the actual total resistance is $2.40 Ohm,$ find the range of percentage error in R.

The following table gives the masses of the various particles that make up an atom.

Calculate the percentage error in taking the mass of an electron to be $(1\times {10}^{-30})kg$.

In an electric circuit, the resistance (R Ohms) of a component may be calculated using the formula $R=\frac{V}{I}$, where V is the potential difference across the component and I is the current through the component. 

The potential difference is measured as 6V to the nearest volt, and the circuit is measured as $.2A$ to the nearest tenth of an Ampere.

The actual value of the resistor is $30 Ohm.$ Calculate the maximum possible percentage error that could be obtained.