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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 $a=1.00 \pm 0.01 \,m / s ^2$, respectively. Then, the mass of the object is ............... $kg$
$10.0$
$10.0 \pm 0.1$
$10.0 \pm 0.3$
$10.0 \pm 0.4$
Solution
(c)
As, force $F=m a$
$\Rightarrow \frac{\Delta F}{F}=\frac{\Delta m}{m}+\frac{\Delta a}{a} \Rightarrow \frac{\Delta m}{m}=\frac{\Delta F}{F}-\frac{\Delta a}{a}$
$\Rightarrow \frac{\Delta m}{m}=\left(\frac{\pm 0.2}{10}\right)-\left(\frac{\pm 0.01}{1}\right)$
So, $\left(\frac{\Delta m}{m}\right)_{\max }=\frac{0.2}{10}+\frac{0.01}{1}=0.03$
Maximum error in mass occurs when error in force and acceleration are of different signs.
So, $\Delta m=0.03 \times m=0.03 \times 10 \Rightarrow \Delta m=0.3\, kg$
Hence, mass of object is $m=10 \pm 0.3 \,kg$.
