Embibe Experts Solutions for Exercise 3: Assignment

The kinetic energy of a particle depends on the square of speed of the particle. If error in measurement of speed is $30\%$, the error in the measurement of kinetic energy will be $n\%$. The value of $n$ is _____.

To determine the Young's modulus of a wire, the formula is $Y=\frac{F}{A}\times \frac{L}{\Delta L}$ where $L=$ length; $A=$ area of cross-section of the wire, $\Delta L=$change in length of the wire when stretched with a force $F$. The conversion factor to change it from $CGS$ to $MKS$ system is $n$. The value of $n$ is

A wire has a mass $(0.3\pm 0.003)\mathrm{g}$, radius $(0.5\pm 0.005)\mathrm{mm}$ and length $(6\pm 0.06)\mathrm{cm}$. The maximum percentage error in measurement of density is $n$. The value of $n$ is _____.

The percentage error in measurement of a physical quantity $m$, given by $m=\pi \tan \theta$, is minimum when $\theta =n°$. The value of $n$ is _____.

The number of significant figures in $(3.20+4.80)$ $\times {10}^5$ is _____.

A student performs experiment with simple pendulum and measures time for $10$ vibrations. If he measures a time for $100$ vibrations, the relative error in measurements of time period will be reduced by $n\%$. The value of $n$ is

Intensity observed in an interference pattern is $I=I_0 {\sin }^2\mathrm{\theta }$. At $\mathrm{\theta }=30°$, intensity $I=5\pm 0.002$. The percentage error in angle if $I_0=20 \mathrm{W} {\mathrm{m}}^{-2}$ is $\frac{\sqrt{n}}{\mathrm{\pi }} \times {10}^{-2}$. Value of $n$, is

The energy of a system as a function of time $t$is given as$E\left(t\right) = A^2 \exp (-\alpha t)$, where $\mathrm{\alpha }= 0.2 {\mathrm{s}}^{-1}$. 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 $E\left(t\right)$ at $t=5 \mathrm{s}$, is