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A wire has a mass (0.3pm0.003) g, radius...

A wire has a mass `(0.3pm0.003)` g, radius `(0.5pm0.005)` mm and length `(6pm0.06)`cm. The maximum percentage error in the measurement of its density is

A

`4%`

B

`3%`

C

`2%`

D

`1%`

Text Solution

Verified by Experts

The correct Answer is:
a
Density `(rho)=("mass")/("volume")=(m)/(pir^(2)L)`
`therefore ((Deltarho)/(rho))xx100=[((Deltam)/(m))+2((Deltar)/(r))+((DeltaL)/(L))]xx100`
`=[(3xx10^(-3))/(3xx10^(-1))+2xx(5xx10^(-3))/(5xx10^(-1))+(6xx10^(-2))/(6)]xx100`
`=[1xx10^(-2)+2xx10^(-2)+1xx10^(-2)]xx100=4`
`therefore` Maximum percentage error in density = 4%
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