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

If the absolute error is $0.05 \ m$ for a measured length of $5 \ m$, what is the percentage error (in $\%$)?

In an experiment,four quantities $a, b, c, d$ are measured with percentage errors $2\%$,$1\%$,$3\%$ and $5\%$,respectively. Quantity $P$ is calculated as $P = \frac{a^2 b^2}{c d}$. Find the percentage error in measuring $P$. (in $\%$)

The period of oscillation of a simple pendulum is $T = 2 \pi \sqrt{\frac{L}{g}}$. The measured value of $L$ is $1.0 \text{ m}$ using a meter scale with a minimum division of $1 \text{ mm}$,and the time for one complete oscillation is $1.95 \text{ s}$ measured using a stopwatch with a resolution of $0.01 \text{ s}$. The percentage error in the determination of $g$ will be ..... $\%$.

The time period of a simple harmonic oscillator is $T = 2 \pi \sqrt{\frac{m}{k}}$. The measured value of mass $(m)$ of the object is $10 \ g$ with an accuracy of $10 \ mg$, and the time for $50$ oscillations of the spring is found to be $60 \ s$ using a watch of $2 \ s$ resolution. The percentage error in the determination of the spring constant $(k)$ is . . . . . . %.

To find the spring constant $(k)$ of a spring experimentally,a student commits $2 \%$ positive error in the measurement of time and $1 \%$ negative error in the measurement of mass. The percentage error in determining the value of $k$ is (in $\%$)