Q42 / 60 · KVPY 2015 (SA) · Physics
In an experiment, mass of an object is measured by applying a known force on it, and then measuring its acceleration. IF, in the experiment, the measured values of applied force and the measured acceleration are $F=10.0 \pm 0.2 N$ and $a=1.00 \pm 0.01$ $\mathrm{m} / \mathrm{s}^{2}$, respectively, the mass of the object is
- A$10.0 \mathrm{Kg}$
- B$10.0 \pm 0.1 \mathrm{Kg}$
- Correct answerC$10.0 \pm 0.3 \mathrm{Kg}$
- D$10.0 \pm 0.4 \mathrm{Kg}$
Solution
$\mathrm{F}=\mathrm{Ma}$
$\mathrm{M}=\frac{\mathrm{f}}{\mathrm{a}}$
$\frac{\Delta \mathrm{M} \times 100}{\mathrm{M}}=\frac{\Delta \mathrm{f}}{\mathrm{f}} \times 100+\frac{\Delta \mathrm{a}}{\mathrm{a}} \times 100$
$\quad=\frac{0.2}{10}+\frac{0.01}{1}$
$\quad \Delta \mathrm{M}=0.03 \times 10$
$\therefore \mathrm{M}=10 \pm 0.3 \mathrm{~kg}$
Hence, the correct answer is option: 'C'.