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 percentage error in the measurement of its angular momentum $(J=I \omega)$ about geometrical axis.

✓

Answer

Angular momentum $(J)=I \omega=\frac{1}{2} M R^{2} \omega$ $\therefore \frac{\Delta J}{J} \times 100=\frac{\Delta M}{M} \times 100+\frac{\Delta \omega}{\omega} \times 100$

$=2 \%+(2 \times 1 \%)+1 \%=5 \%$

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