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1. units,dimensions and measurement — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics1. units,dimensions and measurement1 Mark
MCQ
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 rotational kinetic energy $\left(K=\frac{1}{2} I \omega^{2}\right)$
  • A
    $3$
  • ✓
    $6$
  • C
    $4$
  • D
    $1$
✓

Answer

Correct option: B.
$6$
b
Rotational kinetic energy $(K)=\frac{1}{2} I \omega^{2}=\frac{1}{2} M R^{2} \omega^{2}$

$\therefore \frac{\Delta K}{K} \times 100=\frac{\Delta M}{M} \times 100+2 \frac{\Delta R}{R} \times 100+2 \frac{\Delta \omega}{\omega} \times 100$

$=2 \%+(2 \times 1 \%)=6 \%$

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