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A certain body weighs 22.42 g and has a ...

A certain body weighs `22.42 g` and has a measured volumen of `4.7 c c`. The possible error in the measurement of mass and volumen are `0.01g` and `0.1 c c`. Then, maximum error in the density will be

A

0.22

B

0.022

C

0.002

D

0.0002

Text Solution

Verified by Experts

The correct Answer is:
B
Density, `(rho)=("mass(m)")/("volume(V)")" "......(i)`
Take logarithm to take base e on the both sides of eqn (i), we get
`lnrho=lnm-lnV" "......(ii)`
Differentiate eqn (ii), on both sides, we get
`(Deltarho)/(rho)=(Deltam)/(m)+(DeltaV)/(V)` [Errors are always added]
Maximum error in the density `rho` will be
`=[(Deltam)/(m)+(DeltaV)/(V)]xx100%=[(0.01)/(22.42)+(0.1)/(4.7)]xx100%`
=2.2%
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