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 ...........$\%$
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The density of a material in $SI$ units is $128\, kg\, m^{-3}.$ In certain units in which the unit of length is $25\, cm$ and the unit of mass $50\, g$, the numerical value of density of the material is
A physical quantity is given by $X = {M^a}{L^b}{T^c}$. The percentage error in measurement of $M,L$ and $T$ are $\alpha ,\beta $ and $\gamma $ respectively. Then maximum percentage error in the quantity X is
$Assertion$: In the measurement of physical quantities direct and indirect methods are used.
$Reason$ : The accuracy and precision of measuring instruments along with errors in measurements should be taken into account, while expressing the result.
If $L,\,C$ and $R$ represent inductance, capacitance and resistance respectively, then which of the following does not represent dimensions of frequency
A screw gauge has some zero error but its value is unknown. We have two identical rods. When the first rod is inserted in the screw, the state of the instrument is shown by diagram $(I).$ When both the rods are inserted together in series then the state is shown by the diagram $(II).$ What is the zero error of the instrument ? .......... $mm$
In the equation $y = pq$ $tan\,(qt)$, $y$ represents position, $p$ and $q$ are unknown physical quantities and $t$ is time. Dimensional formula of $p$ is