The temperatures of two bodies measured by a thermometer are t₁ = 20°C ± 0.5°C and t₂ = 50°C ± 0.5°C. Calculate the temperature difference and the error therein.

The correct answer/option is 30°C ± 1°C.

To find the temperature difference and the error therein, we follow the rules of error propagation.
Let the measured temperatures of the two bodies be:
$t_1=20\mathrm{°C}\pm 0.5\mathrm{°C}$
$t_2=50\mathrm{°C}\pm 0.5\mathrm{°C}$

Step 1: Calculate the temperature difference (t)
The temperature difference between the two bodies is given by:
$t=t_2-t_1$
Substituting the nominal values:
$t=50\mathrm{°C}-20\mathrm{°C}=30\mathrm{°C}$

Step 2: Calculate the error in the temperature difference (Δt)
When two quantities are added or subtracted, their absolute errors are always added to find the maximum possible error in the result.
The formula for the error in the difference is:
$\mathrm{\Delta t}={\mathrm{\Delta t}}_1+{\mathrm{\Delta t}}_2$
Given:
${\mathrm{\Delta t}}_1=0.5\mathrm{°C}$
${\mathrm{\Delta t}}_2=0.5\mathrm{°C}$
Substituting these values:
$\mathrm{\Delta t}=0.5\mathrm{°C}+0.5\mathrm{°C}=1.0\mathrm{°C}$

Conclusion:
Combining the temperature difference and its error, we get:
$\mathrm{Temperature\; Difference}=30\mathrm{°C}\pm 1\mathrm{°C}$