Embibe Experts Solutions for Chapter: Physical World and Measurement, Exercise 1: Exercise-1

Which of the following pairs does not have similar dimensions?

Using screw gauge, the observation of the diameter of a wire are $1.324,1.326,1.334,1.336 \mathrm{cm}$ respectively. Find the average diameter, the mean error, the relative error and $\%$ error.

You are given two unknown resistors $X$ and $Y$ These resistances are to be determined, using an ammeter of $R_A=0.5 \mathrm{\Omega }$ and a voltmeter of $R_v=20 \mathrm{k\Omega }$. It is known that $X$ is in range of a few ohms and $Y$ is in the range of several kilo ohm's. Which circuit is preferable to measure $X$ and $Y$.

$\begin{array}{r}\text{ Resistor }\\ X\\ \mathrm{y}\end{array}\begin{array}{r}\text{ Circuit }\\ a\\ \mathrm{b}\end{array}$

Two resistances are measured in Ohm.
$R_1=3\mathrm{\Omega }\pm 1\%$
${\mathrm{R}}_2=6\mathrm{\Omega }\pm 2\%$
When they are connected in parallel, maximum percentage error in equivalent resistance is $\alpha$. Find $3\alpha$.

A student performs an experiment for determination of $g\left(=\frac{4{\pi }^2\ell }{{\mathrm{T}}^2}\right),\ell \approx 1 \mathrm{m}$, and he commits an error of $\Delta \ell$. For $\mathrm{T}$ he takes the time of n oscillations with the stop watch of least count $\Delta T^{\text{'}}$ and he commits a human error of $0.1\sec$. For which of the following data, the measurement of $g$ will be most accurate?

A vernier calipers has $1 \mathrm{mm}$ marks on the main scale. It has $20$ equal division on the Vernier scale which match with $16$ main scale divisions. For this Vernier calipers, the least count is:

Unit of diploe moment is:

An experiment measures quantities $a, b, c$ and $x$ is calculated from $x=\frac{a{b}^2}{c^3}.$ If the percentage errors in $a, b, c$ are $\pm 1\%,\pm 3\%$ and $\pm 2\%$ respectively.