The maximum percentage errors in the measurement of mass (M), rad… - Vidyadip

Question

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.

✓

Answer

Moment of inertia ${\rm{(I) = M}}{{\rm{R}}^{\rm{2}}}{\rm{ }}$

$\therefore \,\,\frac{{\Delta I}}{I}\,\, \times \,\,100\,\, = \,\,\frac{{\Delta M}}{M}\,\, \times \,\,100\,\, + \;\;2\frac{{\Delta R}}{R}\,\, \times \,\,100$

$\, = \,\,2\% \,\, + \;\,\left( {2\,\, \times \,\,1\% } \right)\,\, = \,\,4\% $

the maximum percenta $\, = \,\,4\% $

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