Question

Measure of two quantites along with the precision of respective measuring instrument is `A = 2.5 ms^(-1) +- 0.5 ms^(-1)`
`B = 0.10 s +- 0.01s` The value of AB will be
A. `(0.25+-0.08)m`
B. `(0.25 +- 0.5)`
C. `0.25 +- 0.05)m`
D. `(0.25 +- 0.135)m`

Answer 1

Correct Answer - (a)
Here, `A = 2.5ms^(-1) +- 0.5 ms^(-1), B = 0.10 s +- 0.01s`
`x = AB = (2.5) (1.10) = 0.25m`
`(Deltax)/(x) = (DeltaA)/(A) +(DeltaB)/(B) = (0.5)/(2.5) + (0.01)/(0.10) = (0.05 + 0.025)/(0.25) = (0.075)/(0.25)`
`Deltax =0.075 = 0.08m,` rounding off to two significant figures.
`AB = (0.25 +- 0.08)m.`