Measure of two quantities along with the precision of respective measuring instrument is `A=2.5ms^(-1)+-0.5ms^(-1)`,B=0.10s+-0.01s`. The value of AB will be

Options

A. `(0.25 +- 0.08)m`
B. `(0.25 +- 0.5)m`
C. `(0.25 +- 0.05)m`
D. `(0.25 +- 0.135)m`

Answer

a

Explanation

`A = 2.5ms^(-1) +- 0.5ms^(-1) ,B = 0 10s`
`x = AB = (2.5)(0.10) = 0.25m`
`(Delta x)/(x) = (Delta A)/(A) + (Delta B)/(B)`
`(0.2)/(2.5) + (0.01)/(0.10) = (0.05 + 0.025)/(0.25) = (0.075)/(0.25)`
`Delta x = 0.075 = 0.08m`
Rounding off to two significant figure
`AB = (0.25 +- 0.08)m`