Errors in Measurement

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

The percentage errors in the measurement of mass and speed are  $2\%$ and  $3\%$  respectively. The error in kinetic energy obtained by measuring mass and speed will be:

In a vernier calliper $N$ divisions of vernier scale coincides with$(N-1)$  divisions of the main scale (in which length of one division is $1 \mathrm{mm}$). The least count of the instrument should be (in $\mathrm{cm}$):

A certain body weighs 22.42 gm and has a measured volume of 4.7 cc. The possible error in the measurement of mass and volume are 0.01 gm and 0.1 cc. Then maximum error in the density will be

A certain body weigh 22.42 gm and has a measured volume of 4.7 cc. The possible error in the measurement of mass and volume are 0.01 gm and 0.1 cc. Then maximum error in the density will be

Assertion : When percentage errors in the measurement of mass and velocity are $1\%$ and $2\%$ respectively, the percentage error in K.E. is $5\%$.

Reason :  $\frac{\Delta E}{E}=\frac{\Delta m}{m}+\frac{\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}2\Delta v}{v}$

Assertion: When percentage errors in the measurement of mass and velocity are $1\%$ and $2\%$, respectively, the percentage error in Kinetic Energy is $5\%$. 

Reason:  $\frac{\Delta E}{E}=\frac{\Delta m}{m}+\frac{\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}2\Delta v}{v}$ (where $E$ is the kinetic energy, $m$ is the mass and $v$ is the velocity). 

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

A student performs an experiment for determination of $g\left(=\frac{4{\pi }^{2}l}{T^2}\right)$. The error in length $l$ is $\mathrm{\Delta }l$ and in time $T$ is $\mathrm{\Delta }T$ and $n$ is number of times the reading is taken. The measurement of $g$ is most accurate for

In Searle’s experiment, which is used to find Young’s Modulus of elasticity, the diameter of experimental wire is $D=0.05cm$ (measured by a scale of least count  $0.001cm$ ) and length is  $L=110cm$  (measured by a scale of least count $0.1cm$ ). A weight of 50 N causes an extension of  $X=0.125cm$  (measured by a micrometer of least count $0.001cm$ ). Find maximum possible error in the values of Young’s modulus. Screw gauge and meter scale are free from error.

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.