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. `1.98 xx 10^(-1) mm`
B. `1.98 xx 10^(-2)mm`
C. `1.98 xx 10^(-3)mm`
D. `1.98 xx 10^(-4)mm`

Explanation

True measurement =scale reading `[1 + alpha (theta - theta_(0))]`
`= 180 [1- 10 xx 1.1 xx 10^(-5)]`
error `= 180 - 180 [1-1.1 xx 10^(-4)] = 1.98 xx 10^(-2) mm`