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A physical quantity $P$ is given by $P= \frac{{{A^3}{B^{\frac{1}{2}}}}}{{{C^{ - 4}}{D^{\frac{3}{2}}}}}$. The quantity which brings in the maximum percentage error in $P$ is
In an experiment to find acceleration due to gravity $(g)$ using simple pendulum, time period of $0.5\,s$ is measured from time of $100$ oscillation with a watch of $1\;s$ resolution. If measured value of length is $10\; cm$ known to $1\; mm$ accuracy. The accuracy in the determination of $g$ is found to be $x \%$. The value of $x$ is
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
Assertion : The error in the measurement of radius of the sphere is $0.3\%$. The permissible error in its surface area is $0.6\%$
Reason : The permissible error is calculated by the formula $\frac{{\Delta A}}{A} = \frac{{4\Delta r}}{r}$