The time period of a simple pendulum is given by $T =2 \pi \sqrt{\frac{\ell}{ g }}$. The measured value of the length of pendulum is $10\, cm$ known to a $1\, mm$ accuracy. The time for $200$ oscillations of the pendulum is found to be $100$ second using a clock of $1s$ resolution. The percentage accuracy in the determination of $'g'$ using this pendulum is $'x'$. The value of $'x'$ to the nearest integer is ...........$\%$

The maximum error in the measurement of resistance, current and time for which current flows in an electrical circuit are $1 \%, 2 \%$ and $3 \%$ respectively. The maximum percentage error in the detection of the dissipated heat will be

The random error in the arithmetic mean of $100$ observations is $x$; then random error in the arithmetic mean of $400$ observations would be

In a experiment to measure the height of a bridge by dropping a stone into water underneath, if the error in the measurement of times is $0.1\;s$ at the end of $2\;s$, then the error in the estimation of the height of the bridge will be

$Assertion$ : When percentage errors in the measurement of mass and velocity are $1\%$ and $2\%$ respectively, the percentage error in $K.E.$ is $5\%$.

$Reason$ : $\frac{{\Delta E}}{E} = \frac{{\Delta m}}{m} + \frac{{2\Delta v}}{v}$

If radius of the sphere is $(5.3 \pm 0.1)\;cm$. Then percentage error in its volume will be