In an experiment,the percentage errors in the | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given the expression for $X$ is $X = \frac{A^2 B^{1/2}}{C^{1/3} D^3}$.The relative error in $X$ is given by the formula: $\frac{\Delta X}{X} = 2 \

Vedclass · Accepted Answer

$16 \%$

Vedclass · Answer

(B) Given the expression for $X$ is $X = \frac{A^2 B^{1/2}}{C^{1/3} D^3}$.The relative error in $X$ is given by the formula: $\frac{\Delta X}{X} = 2 \frac{\Delta A}{A} + \frac{1}{2} \frac{\Delta B}{B} + \frac{1}{3} \frac{\Delta C}{C} + 3 \frac{\Delta D}{D}$.To find the maximum percentage error,we multiply by $100$:$\frac{\Delta X}{X} 	imes 100 = 2 \left( \frac{\Delta A}{A} 	imes 100 ight) + \frac{1}{2} \left( \frac{\Delta B}{B} 	imes 100 ight) + \frac{1}{3} \left( \frac{\Delta C}{C} 	imes 100 ight) + 3 \left( \frac{\Delta D}{D} 	imes 100 ight)$.Substituting the given percentage errors $(1\%, 2\%, 3\%, 4\%)$:$\frac{\Delta X}{X} 	imes 100 = 2(1\%) + \frac{1}{2}(2\%) + \frac{1}{3}(3\%) + 3(4\%)$.Calculating the values:$= 2\% + 1\% + 1\% + 12\% = 16\%$.Thus,the maximum percentage error in $X$ is $16\%$.

In an experiment,the percentage errors in the measurement of physical quantities $A, B, C,$ and $D$ are $1\%, 2\%, 3\%,$ and $4\%$ respectively. The maximum percentage error in the measurement of $X,$ where $X = \frac{A^2 B^{1/2}}{C^{1/3} D^3},$ will be:

Similar Questions

In a typical combustion engine,the work done by a gas molecule is given by $W = \alpha^{2} \beta e^{\frac{-\beta x^{2}}{kT}}$,where $x$ is the displacement,$k$ is the Boltzmann constant,and $T$ is the temperature. If $\alpha$ and $\beta$ are constants,the dimensions of $\alpha$ will be:

If the unit of force is $1 \,kN$,the unit of length is $1 \,km$,and the unit of time is $100 \,s$,what will be the unit of mass in $kg$?

What could be a correct expression for the speed of ocean waves in terms of its wavelength $\lambda$,the depth $h$ of the ocean,the density $\rho$ of sea water,and the acceleration of free fall $g$?

The equation of state for some gases is given by $(P + \frac{a}{V^2})(V - b) = RT$,where $P$ is pressure,$V$ is volume,$T$ is absolute temperature,and $a, b, R$ are constants. What are the dimensions of '$a$'?

The refractive index of the medium is $\mu = A + \frac{B}{\lambda^{2}}$,where $A$ and $B$ are constants and $\lambda$ is the wavelength of light. The dimensions of $B$ are the same as that of

Vedclass Test Series

Exam Paper Generator

Online Exam Module