A physical quantity 'x' is calculated from the relation x = frac{{{a^2}{b^3}}}{{csqrt d }} in a,b,c and d are 2%, 1 %, 3% and 4%

Q: 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 $x$.

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

SECTION - A [PHYSICS MCQ]

GSEB - English Medium

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\%$
C$ \pm 12\%$
D$ \pm 14\%$

Medium

STD 11 Science
JEE
STD 11 - 1. units,dimensions and measurement
Physics

Download our app
and get started for free

Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*

Download App

Similar Questions

1
The unit of length, velocity and force are doubled. Which of the following is the correct change in the other units?
View Solution
2
Dimensions of luminous flux are
View Solution
3
The order of the magnitude of speed of light in $SI$ unit is ........
View Solution
4
In terms of resistance $R$ and time $T$, the dimensions of ratio $\frac{\mu } {\varepsilon }$ of the permeability $\mu $ and permittivity $\varepsilon $ is
View Solution
5
if Energy is given by $U = \frac{{A\sqrt x }}{{{x^2} + B}},\,$, then dimensions of $AB$ is
View Solution
6
The dimensional formula of farad is
View Solution
7
There are $100$ divisions on the circular scale of a screw gauge of pitch $1 \mathrm{~mm}$. With no measuring quantity in between the jaws, the zero of the circular scale lies $5$ divisions below the reference line. The diameter of a wire is then measured using this screw gauge. It is found the $4$ linear scale divisions are clearly visible while $60$ divisions on circular scale coincide with the reference line. The diameter of the wire is :
View Solution
8
Two quantities $A$ and $B$ have different dimensions. Which mathematical operation given below is physically meaningful
View Solution
9
Given below are two statements :

$Statement$ $(I)$ : Planck's constant and angular momentum have same dimensions.

$Statement$ $(II)$ : Linear momentum and moment of force have same dimensions.

In the light of the above statements, choose the correct answer from the options given below :
View Solution
10
Let $[ {\varepsilon _0} ]$ denote the dimensional formula of the permittivity of vacuum. If $M =$ mass, $L=$ length, $T =$ time and $A=$ electric current, then:
View Solution

Download our appand get started for free

Similar Questions

Download our app
and get started for free