Question

percentage error in measuring the radius and mass of a solid sphere are 2% & 1% respectively. the error in measurement of moment of inertia with respect to its diameter ?

Answer 1

Dear student
$$\begin{gathered} I=\frac{2}{5}M{R}^2=\frac{2}{5}M{\left(\frac{D}{2}\right)}^2=\frac{2}{5}M\left(\frac{D^2}{4}\right)=\frac{2}{20}M\left(\frac{D^2}{1}\right) \\ \frac{∆I}{I}=\frac{∆M}{M}+\frac{2∆D}{D} \\ \%I=\%M+2\%D=1+2\times 2=5\%\{\sin cethe\%errorindiameterissameasradius) \\ Regards \end{gathered}$$