What is called as relative error ? Define fractional error.

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A body of mass $(5 \pm 0.5) kg$ is moving with a velocity of $(20 \pm 0.4) m / s$. Its kinetic energy will be

  • [JEE MAIN 2023]

An experiment is performed to obtain the value of acceleration due to gravity $g$ by using a simple pendulum of length $L$. In this experiment time for $100\, oscillations$ is measured by using a watch of $1\, second$ least count and the value is $90.0\, seconds$. The length $L$ is measured by using a meter scale of least count $1\, mm$ and the value is $20.0\, cm$. The  error in the determination of $g$ would be  ........... $\%$

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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 respectively $1.5\%$ and $1\%$, the maximum error in determining the density is   ........ $\%$

  • [JEE MAIN 2018]

The period of oscillation of a simple pendulum is given by $T = 2\pi \sqrt {\frac{l}{g}} $ where $l$ is about $100 \,cm$ and is known to have $1\,mm$ accuracy. The period is about $2\,s$. The time of $100$ oscillations is measured by a stop watch of least count $0.1\, s$. The percentage error in $g$ is ......... $\%$

Students $I$, $II$ and $III$ perform an experiment for measuring the acceleration due to gravity $(g)$ using a simple pendulum.

They use different lengths of the pendulum and /or record time for different number of oscillations. The observations are shown in the table.

Least count for length $=0.1 \mathrm{~cm}$

Least count for time $=0.1 \mathrm{~s}$

Student Length of the pendulum $(cm)$ Number of oscillations $(n)$ Total time for $(n)$ oscillations $(s)$ Time period $(s)$
$I.$ $64.0$ $8$ $128.0$ $16.0$
$II.$ $64.0$ $4$ $64.0$ $16.0$
$III.$ $20.0$ $4$ $36.0$ $9.0$

If $\mathrm{E}_{\mathrm{I}}, \mathrm{E}_{\text {II }}$ and $\mathrm{E}_{\text {III }}$ are the percentage errors in g, i.e., $\left(\frac{\Delta \mathrm{g}}{\mathrm{g}} \times 100\right)$ for students $\mathrm{I}, \mathrm{II}$ and III, respectively,

  • [IIT 2008]