The acceleration due to gravity is measured on the surface of earth by using a simple pendulum. If $\alpha$ and $\beta$ are relative errors in the measurement of length and time period respectively, then percentage error in the measurement of acceleration due to gravity is ................
$\left(\alpha+\frac{1}{2} \beta\right) \times 100$
$(\alpha-2 \beta)$
$(2 \alpha+\beta) \times 100$
$(\alpha+2 \beta) \times 100$
Time intervals measured by a clock give the following readings :
$1.25 \;s , 1.24\; s , 1.27\; s , 1.21 \;s$ and $1.28\; s$
What is the percentage relative error of the observations?
A body travels uniformly a distance of $ (13.8 \pm 0.2) m$ in a time $(4.0 \pm 0.3)\, s$. The velocity of the body within error limits is
An experiment measures quantities $a, b$ and $c$, and quantity $X$ is calculated from $X=a b^{2} / c^{3}$. If the percentage error in $a$, $b$ and $c$ are $\pm 1 \%, \pm 3 \%$ and $\pm 2 \%$, respectively, then the percentage error in $X$ will be
The length, breadth and thickness of a strip are $(10.0 \pm 0.1)\; cm ,(1.00 \pm 0.01) \;cm$ and $(0.100 \pm 0.001)\; cm$ respectively. The most probable error in its volume will be?
Two resistance are measured in $Ohm$ and is given as
$R_1 = 3 \Omega \pm 1\%$ and $R_2 = 6 \Omega \pm 2\%$ When they are connected in parallel, the percentage error in equivalent resistance is.......... $\%$