A bar measured with a vernier caliper is found to be 180 mm long. The temperature during the measurement is `10^@C`. The measurement error will be if the scale of the vernier caliper has been graduated at a temeprature of `20^@C`. (`alpha=1.1xx10^(-5).^(@)C^(-1)`. Assume that the length of the bar does not change.)

Options

A. `1.98xx10^-1mm`
B. `1.98xx10^-2mm`
C. `1.98xx10^-3mm`
D. `1.98xxx10^-4mm`

Answer

B

Explanation

True measurement`=`scale reading
`[1+alpha(theta-theta_0)]=180xx{1+(10-20)xx(-1.1xx10^-5)}`
Measurement error`=`true measurement`-`scale reding
`=180xx{1+(10-20)xx(-1.1xx10^-5)}-180`
`=1.98xx10^-2mm`