Error Analysis

If two lengths $a$ and $b$ are given as : $a=25.4 \mathrm{cm}\pm 0.1 \mathrm{cm}$ and $b=16.5 \mathrm{cm}\pm 0.4 \mathrm{cm}$.
Then find $a+b$.

A physical quantity is represented by $[X]=\left[ M^{a}L^{b}T^{-c} \right]$. If percentage error in the measurement of M, L and T are $\alpha\%,\beta\%$ and $\gamma\%$ respectively, then total percentage error is

$The pressure on a square plate is measured by measuring the force acting on the plate and length of the sides of the plate. The maximum error in the measurement of force and length are respectively 4\% and 2\%, the percentage error in the measurement of pressure is$

If $Z=\dfrac{A^{4}B^{1/3}}{CD^{3/2}}$ and $\Delta A,\Delta B,\Delta C$, and $\Delta D$ are their absolute errors in $A,B,C$ and $D$ respectively. The relative error in $Z$ is

The radius of a ball is $(5.4\pm 0.2)\mathrm{cm}$. The percentage error in the volume of the ball is

In an experiment four quantities $a,b,c$ and $d$ are measured with percentage error $1\%,2\%,3\%$ and $4\%$ respectively. Quantity $P$ is calculated as follows $P=\dfrac{a^{3}b^{2}}{cd}\%$ error in $P$ is

The percentage error in the measurement of mass of a body and its speed are $0.73 \%$ and $1.84 \%$ respectively. The percentage error in the measurement of its momentum and kinetic energy are respectively

A quantity P is related as $X^{-2} Y^{-3 / 2} Z^{2 / 5}$ where X,Y,Z are independent parameters which have fractional errors of 0.1, 0.2 and 0.5 respectively in measurement. The maximum fractional error in $P$ is

The error in the measurement of length and mass of a cube is 3% and 4% respectively. The error in the measurement of its density will be

If two resistors of resistances have values $R_{1}=(350 \pm 3) \Omega$ and $R_{2}=(140 \pm 4) \Omega$. The percentage error for the sum and difference of $R_{1}$ and $R_{2}$ are respectively

The percentage error in the measurement of mass and speed of a particular body is $3 \%$ and $4 \%$ respectively. The percentage error in the measurement of kinetic energy is

Which of the following comes under the category of random errors?

A force F is applied on a square plate of side L . If the percentage error in determining F is $3 \%$ and that in L is 2%, then the percentage error in determining the pressure is

A physical quantity ' X ' is related to four measurable quantities ' $a$ ', ' $b$ ', ' $c$ ' and ' $d$ ' as $\mathrm{X}=a^{2} \quad b^{3} c^{5 / 2} \quad d^{-2}$ . The percentage error in the measurement of 'a', 'b', 'c' and 'd' are 1%, 2%, 2% and 4% respectively. The percentage error in measurement of quantity ' X ' is

In order to measure the period of a single pendulum using a stop clock, a student repeated the experiment for 10 times and noted down the time period for each experiment as $5.1, 5.0, 4.9, 4.9, 5.1, 5.0, 4.9, 5.1, 5.0$, 4.9 s. The correct way of expressing the result for the period is