Question

Measure of two quantities along with the precision of respective measuring instrument is :-
A = 2.5 m/s + 0.5 m/s
B = 0.10s + 0.01s
The value of AB will be :-
(1) (0.25 +0.08)m (2) (0.25 + 0.5) m (3) (0.25 + 0.05) m (4) (0.25 +0.135) m​

Answer 1

Answer:

(0.25+0.08)m

Explanation:

AB=A×B = 2.5m/s × 0.10s = 0.25m

(this is correct according to significant figures as the number of significant figures is two(equal to significant figures of A and B ) )

$\frac{d(AB)}{AB} = \frac{d(A)}{A} + \frac{d(B)}{B}$

$\frac{d(AB)}{0.25} = \frac{0.5}{2.5} + \frac{0.01}{0.1}$

$\frac{d(AB)}{0.25} = \frac{1}{5} + \frac{1}{10}$

$\frac{d(AB)}{0.25} = \frac{3}{10}$

$d(AB) = \frac{3}{40} = 0.075$

so, as of now the formula for AB should be :

AB=(0.25+0.075)m

but the problem in the above expression is that the significant figures in 0.075 is more than 0.25 which is not possible as the error and true value must have same number of significant figures.

•°•, the final expression after rounding off will be:

AB= (0.25+0.08)m. [0.075 round off = 0.08]