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

The voltage $V\left(t\right)$ across a capacitor of capacitance $C$ discharging through a resistance $R$ is given by $V\left(t\right)=V_0{e}^{-t/RC}$. The initial voltage $V_0$ is $10.00\pm 0.02 \mathrm{V},R=100.0$ $\pm 0.1\%\mathrm{M}\Omega$ and $C=1.00\mu \mathrm{F}$. The circuit is closed and subsequently disconnected after $100\pm 1$ seconds. The final voltage is best represented as

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:

A body accelerates from rest with a uniform acceleration $a$ for a time $t.$ The uncertainty in '$a$' is $8\%$ and the uncertainty in '$t$' is $4\%.$ The uncertainty in the speed is

The temperature of a metal coin is increased by $100°\mathrm{C}$ and its diameter increases by $0.15\%.$ Its area increases by nearly

The length and width of a rectangular room are measured to be $3.95\pm 0.05 \mathrm{m}$ and $3.05\pm 0.05 \mathrm{m}$, respectively. The area of the floor is

The temperature of a metal coin is increased by $100°\mathrm{C}$ and its diameter increases by $0.15\%.$ Its area increases by nearly

Students $A,B$ and $\mathrm{C}$ measure the length of a room using $25 \mathrm{m}$ long measuring tape of least count $\mathrm{LC}$ $0.5 \mathrm{cm},$ meter-scale of $\mathrm{LC} 0.1 \mathrm{cm}$ and a foot-scale of $\mathrm{LC} 0.05 \mathrm{cm},$ respectively. If the specified length of the room is $9.5 \mathrm{m},$ then which of the following students will report the lowest relative error in the measured length? $\left(1 \mathrm{foot}=30.48 \mathrm{cm}\right)$

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) then the percentage error in measurement of terminal speed of sphere is