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 pm 0.08)m`
B. `(0.25 pm 0.5)m`
C. `(0.25 pm 0.05)m`
D. `(0.25 pm 0.135)m`

Answer

A

Explanation

`A = 2.5 ms^(-1) pm 0.5ms^(-1), B = 0.10 s pm 0.01 s`
`x = AB = (2.5)(0.10) = 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)`
`Delta x =0.075 = 0.08m` , rounding off two significant figures `AB = (0.25 pm 0.08)m.`