NEET Physics Mathematical Tools, Units & Dimensions NEET PYQ-Mathematical Tools, Units and Dimensions

If the error in the measurement of radius of a sphere is. 2%, then the error in the determination of volume of the sphere will be [AIPMPT (S) 2008]

A) 4%

B) 6%

C) 8%

D) 2%

Correct Answer: B

Solution :

Volume of a sphere \[=\frac{4}{3}\pi \] (radius)3

or \[V=\frac{4}{3}\pi {{R}^{3}}\]

Taking logarithm on both sides, we have

\[\log V=\log \frac{4}{3}\pi +3\log R\]

Differentiating, we get \[\frac{\Delta V}{V}=0+\frac{3\Delta R}{R}\]

Accordingly, \[\frac{\Delta R}{R}=2%\]

Thus, \[\frac{\Delta V}{V}=3\times 2%=6%\]