Error Analysis

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.

Area of the cross-section of a wire is measured using a screw gauge. The pitch of the main scale is $0.5 \mathrm{mm}$. The circular scale has $100$ divisions and for one full rotation of the circular scale, the main scale shifts by two divisions. The measured readings are listed below.

What are the diameter and cross-sectional area of the wire measured using the screw gauge?

 If the errors in measurement of the force on a plate and the radius of the plate are$5\%$ and $3\%$ respectively, find the percentage of error in the measurement of pressure.

Find the percentage error in measurement of terminal speed of sphere if the percentage error in measurement of radius of a sphere falling in a viscous liquid is $2\%$ and no error in measurement of other quantity.

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 $2.80 \mathrm{s}$.

The zero error is classified as:

Zero error belongs to the category of :

A physical quantity $P$ is described by the relation $P=a^{\frac{1}{2}} b^2 c^3{d}^{-4}$. If the relative errors in the measurement of $\mathrm{a}$, $\mathrm{b}$, $\mathrm{c}$ and $\mathrm{d}$ respectively, are $2\%$, $1\%$, $3\%$ and $5\%$. Then the relative error in $P$ will be: