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The length and width of a rectangular p...

The length and width of a rectangular plate are `(16.30+-0.05)` and `(13.80+-0.05)` cm respectively. Calculate the area of the plate and also find the uncertainty in the area.

Text Solution

Verified by Experts

`l=(16.30+-0.05)cmDeltal=0.05cm`
`b=(13.80+-0.5)cm, Deltab=0.05cm`
`:.A=16.30xx13.80=224:94`
Relative error in `l=((Deltal)/l)=(0.05/16.30)` Relative errorin `b=((Deltab)/b)=(0.05/13.80)`
`:.` Relative error in area `=((DeltaA)/A)=((Deltal)/l)+((Deltab)/b)=(0.05/16.30)=(1.50/224.94)=0.0067`
Percentage error in area `=0.0064xx100%=0.67%`
`:.` Area of the plate `=(224.94+-1.5)cm^(2)` or `(224.94+-0.67%)cm^(2)`
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