The length and breadth of a rectangle are $(5.7 \pm 0.1) cm$ and $(3.4 \pm 0.2) cm$, respectively. Calculate the area of rectangle with error limits.
$(15.07 \pm 0.18) sq.cm$
$(17.07 \pm 0.98) sq.cm$
$(19.38 \pm 1.48) sq.cm$
$(16.07 \pm 1.18) sq.cm$
A person measures the depth of a well by measuring the time interval between dropping a stone and receiving the sound of impact with the bottom of the well. The error in his measurement of time is $\delta \mathrm{T}=0.01$ seconds and he measures the depth of the well to be $\mathrm{L}=20$ meters. Take the acceleration due to gravity $\mathrm{g}=10 \mathrm{~ms}^{-2}$ and the velocity of sound is $300 \mathrm{~ms}^{-1}$. Then the fractional error in the measurement, $\delta \mathrm{L} / \mathrm{L}$, is closest to
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 physical quantity $Q$ is found to depend on quantities $a, b, c$ by the relation $Q=\frac{a^4 b^3}{c^2}$. The percentage error in $a$, $b$ and $c$ are $3 \%, 4 \%$ and $5 \%$ respectively. Then, the percentage error in $\mathrm{Q}$ is :
The mass and volume of a body are found to be $(5.00 ± 0.05)\,kg$ and $(1.00 ± 0.05)\,m^3$ respectively. Then the maximum possible percentage error in its density is .......... $\%$