BM Sharma Solutions for Chapter: Unit Dimension and Measurement, Exercise 6: DPP

A physical parameter $a$ can be determined by measuring the parameters $b\mathit{,}\mathit{ }c\mathit{,}\mathit{ }d$ and $e$ using the relation, $a=\frac{{\mathit{b}}^{\mathit{\alpha }}{\mathit{c}}^{\mathit{\beta }}}{{\mathit{d}}^{\mathit{\gamma }}{\mathit{e}}^{\mathit{\delta }}}$. If the maximum errors in the measurement of $b, c, d$ and $e$ are $b_1\%, c_1\%, d_1\%$ and $e_1\%$, respectively, then the maximum error in the value of $a$, determined by the experiment is,

The relative density of the material of a body is found by weighing it first in the air and then in water. If the weight in air is $(5.00\pm 0.05) \mathrm{N}$ and weight in water is $(4.00\pm 0.05) \mathrm{N}$, then the relative density, along with the maximum permissible percentage error, is,

The period of oscillation of a simple pendulum in an experiment is recorded as $2.63 \mathrm{s}, 2.56 \mathrm{s}, 2.42 \mathrm{s}, 2.71 \mathrm{s}$ and $2.80 \mathrm{s}$, respectively. The average absolute error is,

The length of a cylinder is measured with a meter rod having least count$0.1 \mathrm{cm}$. Its diameter is measured with vernier caliper having least count $0.01 \mathrm{cm}$. Given that length is $5.0$$\mathrm{cm}$ and radius is $2.0 \mathrm{cm}$, the percentage error in the calculated value of the volume will be,

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

If there is a positive error of $50\%$ in the measurement of the velocity of a body, then the error in the measurement of its kinetic energy is,

A physical quantity $A$ is related to four observables, $a, b, c$ and $d$ as, $A=\frac{a^2{b}^3}{c\sqrt{d}}$. The percentage errors of measurement in $a, b, c$ and$d$are $1\%, 3\%, 2\%$ and  $2\%$, respectively. What is the percentage error in the quantity $A$?

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 the measurement of its density is,