The length of a rectangular plate is measured by a meter scale and is found to be ` 10.0 cm`. Its width is measured by vernier callipers as `1.00 cm`. The least count of the meter scale and vernier calipers are `0.1 cm and 0.01 cm` respectively. Maximum permissibe error in area measurement is.

Options

A. `+-0.2cm^(2)`
B. `+-0.1cm^(2)`
C. `+-0.3cm^(2)`
D. zero

Answer

A

Explanation

(`A`), `A=lxxb`
`implies(dA)/(A)=overset(-)(+)(dl)/(l)overset(-)(+)(db)/(b)=overset(-)(+)(0.1)/(10.0)overset(-)(+)(0.01)/(1.00)`
for max error use positive sign.
`=overset(-)(+)0.01overset(-)(+)0.01`, `((dA)/(A))_(max)=0.02`
`implies(dA)_(max)=0.02xx10.0cm^(2)=0.2cm^(2)`