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

The mass of an object is measured as $225 \pm 0.05 \, g$. Find the percentage error in this measurement. (in $\%$)

What is the percentage error in the measurement of the time period of a pendulum if the maximum errors in the measurement of $l$ and $g$ are $2\%$ and $4\%$ respectively?

Two capacitors with capacitance values $C_1 = 2000 \pm 10 \text{ pF}$ and $C_2 = 3000 \pm 15 \text{ pF}$ are connected in series. The voltage applied across this combination is $V = 5.00 \pm 0.02 \text{ V}$. The percentage error in the calculation of the energy stored in this combination of capacitors is . . . . . .

$A$ wire has mass $(0.3 \pm 0.003) \text{ g}$, radius $(0.5 \pm 0.005) \text{ mm}$ and length $(6 \pm 0.06) \text{ cm}$. The maximum percentage error in the measurement of density is: (in $\%$)

The two specific heat capacities of a gas are measured as $C_P = (12.28 \pm 0.2) \text{ units}$ and $C_V = (3.97 \pm 0.3) \text{ units}$. Find the value of the gas constant $(R)$.