$Assertion$ : 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 $\frac{\Delta A}{A} = \frac{4\Delta r}{r}$.
$Reason$ : The permissible error is calculated by the formula $\frac{\Delta A}{A} = \frac{4\Delta r}{r}$.
- AIf both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.
- BIf both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion.
- CIf the Assertion is correct but Reason is incorrect.
- DIf both the Assertion and Reason are incorrect.
Explore More
Similar Questions
The length and breadth of a rectangle are $(5.7 \pm 0.1) \text{ cm}$ and $(3.4 \pm 0.2) \text{ cm}$,respectively. Calculate the area of the rectangle with error limits.
Medium
View SolutionStudents $I$,$II$,and $III$ perform an experiment for measuring the acceleration due to gravity $(g)$ using a simple pendulum. They use different lengths of the pendulum and/or record time for different numbers of oscillations. The observations are shown in the table. Least count for length $= 0.1 \text{ cm}$. Least count for time $= 0.1 \text{ s}$.
Student Length $(cm)$ Oscillations $(n)$ Total Time $(s)$ Time Period $(s)$ $I$ $64.0$ $8$ $128.0$ $16.0$ $II$ $64.0$ $4$ $64.0$ $16.0$ $III$ $20.0$ $4$ $36.0$ $9.0$
If $E_{I}$,$E_{II}$,and $E_{III}$ are the percentage errors in $g$,i.e.,$(\frac{\Delta g}{g} \times 100)$ for students $I$,$II$,and $III$ respectively,which of the following is correct?
| Student | Length $(cm)$ | Oscillations $(n)$ | Total Time $(s)$ | Time Period $(s)$ |
| $I$ | $64.0$ | $8$ | $128.0$ | $16.0$ |
| $II$ | $64.0$ | $4$ | $64.0$ | $16.0$ |
| $III$ | $20.0$ | $4$ | $36.0$ | $9.0$ |
If $E_{I}$,$E_{II}$,and $E_{III}$ are the percentage errors in $g$,i.e.,$(\frac{\Delta g}{g} \times 100)$ for students $I$,$II$,and $III$ respectively,which of the following is correct?
MediumIIT 2008
View SolutionIf the absolute error is $0.05 \ m$ for a measured length of $5 \ m$, what is the percentage error (in $\%$)?
The density of a cube is measured by measuring its mass and length of its sides. The percentage error in the measurement of mass and length are $5 \%$ and $6 \%$ respectively. The percentage error in the measurement of density is (in $\%$)
$A$ torque meter is calibrated to reference standards of mass,length,and time,each with $5 \%$ accuracy. After calibration,the measured torque with this torque meter will have a net accuracy of $............\%$.
Vedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo