A wire of length `l = +- 0.06cm` and radius `r =0.5+-0.005 cm` and mass `m = +-0.003gm`. Maximum percentage error in density is

Options

A. (a) `4`
B. (b) `2`
C. ( c ) `1`
D. (d) `6.8`

Answer

A

Explanation

(a) `rho = (m)/(l pir^(2))`
`(Deltarho)/(rho) = (Deltam)/(m) + (2pir)/( r ) + (Deltal )/(l )`
Putting the values
`Deltal = 0.06 cm, l = 6cm`, `Deltar = 0.005 cm`, `r = 0.5cm`,
`m= 0.3gm`, `Deltam = 0.003gm`
:. `(Deltarho)/(rho) = (4)/(100)`
:. `(Deltarho)/(rho) xx 100 = 4%`