Error Analysis

To estimate $g$ from $g=4{\pi }^2\frac{L}{T^2}$, error in measurement of $L$ is $\pm 2\mathit{\%}$ and error in measurement of $T$ is $\pm 3\mathit{\%}$. The error in estimated $g$ will be

A student measuring the diameter of a pencil of circular cross-section with the help of a vernier scale records the following four readings $5.50 \mathrm{mm}$, $5.55 \mathrm{mm}$, $5.34 \mathrm{mm}$, $5.65 \mathrm{mm}$. The average of these four reading is $5.5375 \mathrm{mm}$ and the standard deviation of the data is $0.07395 \mathrm{mm}$. The average diameter of the pencil should therefore be recorded as :

A physical quantity z depends on four observables $a, b, c$ and $d$, as  $z=\frac{a^2{b}^{{\displaystyle \frac{2}{3}}}}{\sqrt{c}{d}^3}.$ The percentage of error in the measurement of $a, b, c$ and $d$ are $2\%, 1.5\%, 4\%$  and $2.5\%$ respectively. The percentage of error in $z$ is :

Using screw gauge of pitch $0.1\mathrm{cm}$ and $50$ divisions on its circular scale, the thickness of an object is measured. It should correctly be recorded as,

For a cubical block, error in measurement of sides is $+ 1\%$ and error in measurement of mass is $+ 2\%$, then maximum possible error in density is,

The length of a rectangular plate is measured by a meter scale and is found to be $10.0 \mathrm{cm}$. Its width is measured by vernier calipers as $1.00 \mathrm{cm}$. The least count of the meter scale and vernier calipers are $0.1 \mathrm{cm}$ and $0.01 \mathrm{cm}$, respectively (obviously). Maximum permissible error in area measurement is -

If the error in the measurement of radius of a sphere is 2% then the error in determination of volume of the sphere will be:

The length $l$, breadth $b$ and thickness $t$ of a block of wood were measured with the help of a measuring scale. The results with the permissible errors are $l=\left(15.12\pm 0.01\right) \mathrm{cm}$, $b=\left(10.15\pm 0.01\right) \mathrm{cm}$ and $t=\left(5.28\pm 0.01\right) \mathrm{cm}$. The percentage error in its volume up to $2$ proper figures is

If the error in measuring the diameter of a circle is $4\%$, then the error in the radius of the circle will be

The error in the measurement of the radius of a sphere is $0.1\%$. The error in the measurement of its volume is

The percentage errors in the measurement of mass and speed are $2\%$ and $3\%$, respectively. How much will be the maximum error in the estimation of kinetic energy obtained by measuring mass and speed?

A simple pendulum is being used to determine the value of gravitational acceleration $g$ at a certain place. The length of the pendulum is $25.0 \mathrm{c}\mathrm{m}$ and a stopwatch with $1 \mathrm{s}$ resolution measures the time taken for $40$ oscillations to be $50 \mathrm{s}$. The accuracy in $\mathrm{g}$ is:

In the density measurement of a cube, the mass and edge length are measured as $\left(10.00\pm 0.10\right) \mathrm{k}\mathrm{g}$ and $\left(0.10\pm 0.01\right)\mathrm{ }\mathrm{m},$ respectively. The error in the measurement of density is:

The percentage errors in quantities $P$, $Q$, $R$ and $S$ are $0.5\%$, $1\%$, $3\%$ and $1.5\%$ respectively in the measurement of a physical quantity $\mathrm{A=}\frac{P^3{Q}^2}{\sqrt{R}S}$. The maximum percentage error in the value of $A$ will be:

The relative error in the determination of the surface area of a sphere is $\alpha$. The relative error in the determination of its volume is

The density of a material, in the shape of a cube, is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are $1.5\%$ and $1\%$, respectively, the maximum error in determining the density is:

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 $a$, $b$, $c$ and $d$ respectively, are $2\%$, $1\%$, $3\%$ and $5\%$. Then the relative error in $P$ will be:

A student measures the time period of $100$ oscillations of a simple pendulum four times. The data set is $90 \mathrm{s}$, $91 \mathrm{s}$, $95 \mathrm{s}$ and $92 \mathrm{s}$. If the minimum division in the measuring clock is $1 \mathrm{s}$, then the reported mean time should be: