A body, under the action of a force $\overrightarrow{\mathrm{F}}=6 \hat{\mathrm{i}}-8 \hat{\mathrm{j}}+10…
A body, under the action of a force $\overrightarrow{\mathrm{F}}=6 \hat{\mathrm{i}}-8 \hat{\mathrm{j}}+10 \hat{\mathrm{k}}$, acquires an acceleration of 1 $\mathrm{ms}^{-2}$. The mass of this body must be
$2 \sqrt{10} \mathrm{~kg}$
$10 \mathrm{~kg}$
$20 \mathrm{~kg}$
$10 \sqrt{2} \mathrm{~kg}$
Solution
Key Idea According to Newton's second law of motion, force $=$ mass $\times$ acceleration.
Here,
$\begin{aligned}
\text {Here, } \overrightarrow{\mathrm{F}} & =6 \hat{\mathrm{i}}-8 \hat{\mathrm{j}}+10 \hat{\mathrm{k}} \\
|\mathrm{F}| & =\sqrt{36+64+100} \\
& =10 \sqrt{2} \mathrm{~N} \\
\mathrm{a} & =1 \mathrm{~ms}^{-2} \\
\therefore \quad \mathrm{m} & =\frac{10 \sqrt{2}}{1}=10 \sqrt{2} \mathrm{~kg}
\end{aligned}$