Error in the measurement of radius of the sph | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Step $1$: Recall the formula for the volume of a sphere.$V = \frac{4}{3} \pi r^3$Step $2$: Apply the rule for the propagation of errors.If a quant

Vedclass · Accepted Answer

$6$

Vedclass · Answer

(C) Step $1$: Recall the formula for the volume of a sphere.$V = \frac{4}{3} \pi r^3$Step $2$: Apply the rule for the propagation of errors.If a quantity $Q$ depends on $x$ as $Q = k \cdot x^n$,the relative error is given by $\frac{\Delta Q}{Q} = n \cdot \frac{\Delta x}{x}$.Therefore,the percentage error is $\frac{\Delta Q}{Q} 	imes 100 \% = n \cdot \left( \frac{\Delta x}{x} 	imes 100 \% ight)$.Step $3$: Apply this to the volume formula.Since $V = \frac{4}{3} \pi r^3$,the volume $V$ is proportional to $r^3$ $(V \propto r^3)$.Thus,the percentage error in $V$ is $\Delta V \% = 3 \cdot \Delta r \%$.Step $4$: Substitute the given value.Given $\Delta r \% = 2 \%$.Therefore,$\Delta V \% = 3 	imes 2 \% = 6 \%$.

Error in the measurement of radius of the sphere is $2 \%$. The error in the calculated value of its volume is (in $\%$)

Similar Questions

$A$ cylindrical wire of mass $(0.4 \pm 0.01) \, g$ has length $(8 \pm 0.04) \, cm$ and radius $(6 \pm 0.03) \, mm$. The maximum error in its density will be $...... \, \%$.

Out of absolute error,relative error,and fractional error,which has a unit and which has no unit?

The resistance $R = \frac{V}{I}$ where $V = (100 \pm 5) \text{ V}$ and $I = (10 \pm 0.2) \text{ A}$. The percentage error in $R$ is: (in $\%$)

The mass of the body is $10.000\,g$ and its volume is $10.00\,cm^3$. If the measured values are expressed up to the correct significant figures,the maximum error in the measurement of density is

The error in the measurement of the radius of a sphere is $1\%$. The error in the calculated value of its volume is ......... $\%$

Vedclass Test Series

Exam Paper Generator

Online Exam Module