The percentage error in measurement of a physical quantity $m$ given by $m = \pi \tan \theta $ is minimum when $\theta $ $=$ ………. $^o$ (Assume that error in $\theta $ remain constant)

The length of a uniform rod is $100.0 \,cm$ and radius is $1.00 \,cm$. If length is measured with a meter rod having least count $1 \,mm$ and radius is measured with vernier callipers having least count $0.1 \,mm$, the percentage error in calculated volume of cylinder is …………. $\%$

The initial and final temperatures of water as recorded by an observer are $(40.6 \pm 0.2)^{\circ} C$ and $(78.9 \pm 0.3)^{\circ} C .$ Calculate the rise in temperature with proper error limits.

Write a note on combination of error.

The internal and external radii of a hollow cylinder are measured with the help of a vernier callipers.Their values are $(4.23 \pm 0.01)\,\,cm$ and $(3.87 \pm 0.01)\,\,cm,$ respectively. The thickness of the wall of the cylinder is