In the density measurement of a cube, the mass and edge length are measured as $(10.00 \pm 0.10)\,\,kg\,$ and $(0.10 \pm 0.01)\,\,m\,$ respectively. The error in the measurement of density is
$0.10\,\,kg/m^3$
$0.31\,\,kg/m^3$
$0.07\,\,kg/m^3$
None of these
If the random error in the arithmetic mean of $50$ observations is $\alpha$, then the random error in the arithmetic mean of $150$ observations would be
A force $F$ is applied on a square area of side $L$. If the percentage error in the measurement of $L$ is $2 \%$ and that in $F$ is $4 \%$, what is the maximum percentage error in pressure is .......... $\%$
Thickness of a pencil measured by using a screw gauge (least count $0.001 \,cm$ ) comes out to be $0.802 \,cm$. The percentage error in the measurement is ........... $\%$
The percentage error in measurement of a physical quantity $m$ given by $m = \pi \tan \theta $ is minimum when $\theta $ $=$ .......... $^o$ (Assume that error in $\theta $ remain constant)
A physical quantity $X$ is given by $X = \frac{{2{k^3}{l^2}}}{{m\sqrt n }}$ The percentage error in the measurements of $k,\,l,\, m$ and $n$ are $1\%, 2\%, 3\%$ and $4\%$ respectively. The value of $X$ is uncertain by .......... $\%$