A physical quantity 'x' is calculated from the relation x = a^2 b… - Vidyadip

MCQ

A physical quantity $'x'$ is calculated from the relation $x = \frac{{{a^2}{b^3}}}{{c\sqrt d }}$ in $a$,$b$,$c$ and $d$ are $2\%$, $1 \%$, $3\%$ and $4\%$ respectively, what is the percentage error in $x$.

A
$ \pm 11\%$
B
$ \pm 13\%$
✓
$ \pm 12\%$
D
$ \pm 14\%$

✓

Answer

Correct option: C.

$ \pm 12\%$

c
$A =\frac{ a ^{2} b ^{3}}{ c \sqrt{ d }}$

$\frac{\Delta a }{ a } \times 100=1 \%,$$ \frac{\Delta b }{ b } \times 100=3 \%,$$ \frac{\Delta c }{ c } \times 100=2 \%$ and $\frac{\Delta d }{ d } \times 100=2 \%$

$\frac{\Delta A }{ A } \times 100=2 \frac{\Delta a }{ a } \times 100+3 \frac{\Delta b }{ b } \times 100+$$\frac{\Delta c }{ c } \times 100+\frac{1}{2} \times \frac{\Delta d }{ d } \times 100$

$\frac{\Delta A }{ A } \times 100=2 \times 2+3 \times 1+3+\frac{1}{2} \times 4=12 \%$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from 1. units,dimensions and measurement→1. units,dimensions and measurement — all question types→Physics STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Carnot cycle (reversible) of a gas represented by a Pressure-Volume curve is shown in the diagramConsider the following statements

$I.$ Area $ABCD =$ Work done on the gas

$II.$ Area $ABCD =$ Net heat absorbed

$III.$ Change in the internal energy in cycle $= 0$

Which of these are correct

In the arrangement, spring constant $k$ has value $2\,N\,m^{-1}$ , mass $M = 3\,kg$ and mass $m = 1\,kg$ . Mass $M$ is in contact with a smooth surface. The coefficient of friction between two blocks is $0.1$ . The time period of $SHM$ executed by the system is

Two particles $X$ and $Y$ having equal charge, after being accelerated through the same potential difference enter a region of uniform magnetic field and describe circular paths of radii $R_1$ and $R_2$ respectively. The ratio of the mass of $X$ to that of $Y$ is:

Projection of vector $\vec A$ on $\vec B$ is

In a system of units if force $(F)$, acceleration $(A) $ and time $(T)$ are taken as fundamental units then the dimensional formula of energy is

The maximum horizontal range of a projectile is $160\, m$. When the projectile is thrown with the same speed at an elevation of $30^o$ from the horizontal, it will reach to the maximum height of ......... $m$

Three blocks $A$, $B$ and $C$ are pulled on a horizontal smooth surface by a force of $80 \mathrm{~N}$ as shown in figure

The tensions $T_1$ and $T_2$ in the string are respectively

Every gas (real gas) behaves as an ideal gas

The resultant of two rectangular simple harmonic motions of the same frequency and equal amplitudes but differing in phase by $\frac{\pi }{2}$ is

A particle is projected from ground with speed $80 \,m / s$ at angle $30^{\circ}$ with horizontal from ground. The magnitude of average velocity of particle in time interval $t=2 \,s$ to $t=6 \,s$ is ....... $m / s$ [Take $g=10 \,m / s ^2$ ]