Find the relative error in $Z,$ if $Z=\frac{A^{4} B^{1 / 3}}{ C D^{3 / 2}}$
Find the relative error in $Z,$ if $Z=\frac{A^{4} B^{1 / 3}}{ C D^{3 / 2}}$
$\text {Answer The relative error in } Z \text { is } \Delta Z / Z=$
$4(\Delta A / A)+(1 / 3)(\Delta B / B)+(\Delta C / C)+(3 / 2)(\Delta D / D)$
Similar Questions
While measuring the acceleration due to gravity by a simple pendulum, a student makes a positive error of $1\%$ in the length of the pendulum and a negative error of $3\%$ in the value of time period. His percentage error in the measurement of $g$ by the relation $g = 4{\pi ^2}\left( {l/{T^2}} \right)$ will be ........ $\%$
While measuring the acceleration due to gravity by a simple pendulum, a student makes a positive error of $1\%$ in the length of the pendulum and a negative error of $3\%$ in the value of time period. His percentage error in the measurement of $g$ by the relation $g = 4{\pi ^2}\left( {l/{T^2}} \right)$ will be ........ $\%$
Two resistors of resistances $R_1 = (300 \pm 3) \,\Omega $ and $R_2 = (500 \pm 4)$ are connected in series. The equivalent resistance of the series combination is
Two resistors of resistances $R_1 = (300 \pm 3) \,\Omega $ and $R_2 = (500 \pm 4)$ are connected in series. The equivalent resistance of the series combination is
Explain effect of multiplication or division of error on final result.
Explain effect of multiplication or division of error on final result.
Explain uncertainty or error in given measurement by suitable example.
Explain uncertainty or error in given measurement by suitable example.
Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$
Assertion $A$ : A spherical body of radius $(5 \pm 0.1)$ $mm$ having a particular density is falling through a liquid of constant density. The percentage error in the calculation of its terminal velocity is $4\,\%$.
Reason $R$ : The terminal velocity of the spherical body falling through the liquid is inversely proportional to its radius.
In the light of the above statements, choose the correct answer from the options given below on :
Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$
Assertion $A$ : A spherical body of radius $(5 \pm 0.1)$ $mm$ having a particular density is falling through a liquid of constant density. The percentage error in the calculation of its terminal velocity is $4\,\%$.
Reason $R$ : The terminal velocity of the spherical body falling through the liquid is inversely proportional to its radius.
In the light of the above statements, choose the correct answer from the options given below on :
- [JEE MAIN 2023]