Question

In some observations, value of 'g' are coming as 9.81, 9.80, 9.82, 9.79, 9.78, 9.84, 9.79, 9.78, 9.79 and 9.80 $m/s^2$.
Calculate absolute errors and percentage error in g.

• A. 'g' = (9.80 $\pm$ 0.014) $m/s^2$
• B. 'g' = (9.8 $\pm$ 0.14) $m/s^2$
• C. 'g' = (9.8 $\pm$ 0.0014) $m/s^2$
• D. 'g' = (9.8000 $\pm$ 0.00014) $m/s^2$

Answer 1

The correct option is A 'g' = (9.80 $\pm$ 0.014) $m/s^2$

S.N.	Value of g	Absolute error $\Delta g=|g_1-\overline{g}|$
1	9.81	0.01
2	9.80	0.00
3	9.82	0.02
4	9.79	0.01
5	9.78	0.02
6	9.84	0.04
7	9.79	0.01
8	9.78	0.02
9	9.79	0.01
10	9.80	0.00
	$g_{mean}=9.80$	$\Delta g_{mean}=\frac{\sum \Delta g_1}{10}$ $=\frac{0.14}{10}=0.014$

Percentage error = $\frac{\Delta g_{mean}}{g_{mean}}\times 100=\frac{0.014}{9.80}\times 100$ % = 0.14 %
so 'g' = (9.80 $\pm$ 0.014) $m/s^2$