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.

Two objects $A$and $B$are of length$5 \mathrm{cm}$ and $7 \mathrm{cm}$ are determined with errors$0.1 \mathrm{cm}$ and $0.2 \mathrm{cm}$ respectively. Error in their total length and difference of their lengths are

A heat engine absorbs heat from a source at $127 °\mathrm{C}$ and rejects a part of heat to sink at temperature $T$ If $T= (27\pm 1) °\mathrm{C}$, then percentage error in measurement of efficiency of heat engine is

. Point out the measurable quantity likely to create the maximum error in the following experimental measurement: Young's Modulus $Y$ of the material of the beam is calculated using the relation $Y=\frac{Wg{l}^3}{4b{d}^3\delta }$ where $W=mg$, $\delta =$depression, $l,b,d$ is length, breadth, thickness.

In an experiment for determination of the focal length of a thin convex lens, the distance of the object from the lens is $10\pm 0.1 \mathrm{cm}$ and the distance of its real image from the lens is $20\pm 0.2 \mathrm{cm}$. The error in the determination of focal length of the lens is $n\%$. The value of $n$ is _____.

The errors in the measurement which arise due to unpredictable fluctuations in temperature and voltage supply are: 

A metal wire has mass ($0.4\pm 0.002$) $\mathrm{g}$, radius ($0.3\pm 0.001$) $\mathrm{mm}$ and length ($5\pm 0.02$) $\mathrm{cm}$. The maximum possible percentage error in the measurement of density will nearly be:

Given below are two statements: one is labelled as

Assertion A and the other is labelled as Reason R

Assertion A : A spherical body of radius $(5 \pm 0.1) \mathrm{mm}$ having a particular density is falling through a liquid of constant density. The percentage error in the calculation of its terminal velocity is $4\%$.

Reason R : The terminal velocity of the spherical body falling through the liquid is inversely proportional to its radius. In the light of the above statements, choose the correct answer from the options given below

A body of mass $(5\pm 0.5) \mathrm{kg}$ is moving with a velocity of $(20\pm 0.4) \mathrm{m} {\mathrm{s}}^{-1}.$ Its kinetic energy will be