$Assertion$ : 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 $\frac{{\Delta A}}{A} = \frac{{4\Delta r}}{r}$
If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.
If both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion.
If the Assertion is correct but Reason is incorrect.
If both the Assertion and Reason are incorrect.
The maximum percentage errors in the measurement of mass (M), radius (R) and angular velocity $(\omega)$ of a ring are $2 \%, 1 \%$ and $1 \%$ respectively, then find the maximum percenta? error in the measurement of its moment of inertia $\left(I=\frac{1}{2} M R^{2}\right)$ about its geometric axis.
The least count of stop watch is $\frac{1}{5}\,second$. The time of $20$ oscillations of pendulum is measured to be $25\,seconds$. Then percentage error in the measurement of time will be.......... $\%$
Write a note on combination of error.
The maximum percentage errors in the measurement of mass $(M)$, radius $(R)$ and angular velocity $(\omega)$ of a ring are $2 \%, 1 \%$ and $1 \%$ respectively, then find the maximum percentage error in the measurement of its angular momentum $(J=I \omega)$ about geometrical axis.
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