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 ..... $\%$.

$A$ student uses a simple pendulum of exactly $1 \ m$ length to determine $g$,the acceleration due to gravity. He uses a stopwatch with a least count of $1 \ s$ for this and records $40 \ s$ for $20$ oscillations. For this observation,which of the following statement$(s)$ is (are) true?
$(A)$ Error $\Delta T$ in measuring $T$,the time period,is $0.05 \ s$
$(B)$ Error $\Delta T$ in measuring $T$,the time period,is $1 \ s$
$(C)$ Percentage error in the determination of $g$ is $5 \%$
$(D)$ Percentage error in the determination of $g$ is $2.5 \%$

The density of a cube is measured by measuring its mass and the length of its sides. If the maximum error in the measurement of mass and length are $4\%$ and $3\%$ respectively,the maximum error in the measurement of density will be ........ $\%$

Explain the error of a sum or a difference.

$A$ metal wire has mass $(0.4 \pm 0.002) \, g$,radius $(0.3 \pm 0.001) \, mm$ and length $(5 \pm 0.02) \, cm$. The maximum possible percentage error in the measurement of density will nearly be $.......\%$

Explain uncertainty or error in a given measurement with a suitable example.