In an experiment, the following observation's were recorded : $L = 2.820\, m, M = 3.00 \,kg, l = 0.087 \,cm$, Diameter $D = 0.041 \,cm$ Taking $g = 9.81$ $m/{s^2}$ using the formula , $Y=\frac{{4MgL}}{{\pi {D^2}l}}$, the maximum permissible error in $Y$ is ......... $\%$

The energy of a system as a function of time $t$ is given as $E(t)=A^2 \exp (-\alpha t)$, where $\alpha=0.2 s ^{-1}$. The measurement of $A$ has an error of $1.25 \%$. If the error in the measurement of time is $1.50 \%$, the percentage error in the value of $E(t)$ at $t=5 s$ is

The dimensional formula for a physical quantity $x$ is $\left[ M ^{-1} L ^{3} T ^{-2}\right]$. The errors in measuring the quantities $M , L$ and $T$ respectively are $2 \%, 3 \%$ and $4 \%$. The maximum percentage of error that occurs in measuring the quantity $x$ is

What is the fractional error in $g$ calculated from $T = 2\pi \sqrt {l/g} $ ? Given fraction errors in $T$ and $l$ are $ \pm x$ and $ \pm y$ respectively?

In an experiment of determine the Young's modulus of wire of a length exactly $1\; m$, the extension in the length of the wire is measured as $0.4\,mm$ with an uncertainty of $\pm 0.02\,mm$ when a load of $1\,kg$ is applied. The diameter of the wire is measured as $0.4\,mm$ with an uncertainty of $\pm 0.01\,mm$. The error in the measurement of Young's modulus $(\Delta Y)$ is found to be $x \times 10^{10}\,Nm ^{-2}$. The value of $x$ is

$\left[\right.$ Take $\left.g =10\,m / s ^{2}\right]$

Write a note on combination of error.