The least count of a stopwatch is $\frac{1}{5} \ s$. The time for $20$ oscillations of a pendulum is measured to be $25 \ s$. The percentage error in the measurement of time will be .......... $\%$

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 ..... $\%$.

$A$ particle covers a distance of $(13.8 \pm 0.2) \ m$ in $(4 \pm 0.3) \ s$. Its velocity under error limits will be

The distance $s$ travelled by a particle in time $t$ is $s = ut - \frac{1}{2} gt^2$. The initial velocity of the particle was measured to be $u = 1.11 \pm 0.01 \, m/s$ and the time interval of the experiment was $t = 1.01 \pm 0.1 \, s$. The acceleration was taken to be $g = 9.8 \pm 0.1 \, m/s^2$. With these measurements,the student estimates the total distance travelled. How should the student report the result?

$A$ student in the laboratory measures the thickness of a wire using a screw gauge. The readings are $1.22\,mm$,$1.23\,mm$,$1.19\,mm$,and $1.20\,mm$. The percentage error is $\frac{x}{121}\%$. The value of $x$ is ..............

If the radius of a sphere is $(5.3 \pm 0.1) \; cm$,then the percentage error in its volume will be: