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

To solve the problem step by step, we will follow the process of calculating the measurement error due to the temperature difference between the measurement of the bar and the calibration of the vernier caliper.

### Step 1: Identify Given Values
- Length of the bar (L₀) = 180 mm
- Initial temperature during measurement (T₁) = 10 °C
- Calibration temperature of the vernier caliper (T₂) = 20 °C
- Coefficient of linear expansion (α) = 1.1 × 10⁻⁵ °C⁻¹

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