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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 $1 \mathrm{~m} / \mathrm{s}^2$. The mass of this body must be :
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Verified Answer
The correct answer is:
$10 \sqrt{2} \mathrm{~kg}$
$$
\begin{aligned}
\overrightarrow{\mathrm{F}} & =6 \hat{\mathrm{i}}-8 \hat{\mathrm{j}}+10 \hat{\mathrm{k}} \\
|\overrightarrow{\mathrm{F}}| & =\sqrt{6^2+8^2+10^2}=10 \sqrt{2} \\
\mathrm{~m} & =\frac{|\overrightarrow{\mathrm{F}}|}{\mathrm{a}}=\frac{10 \sqrt{2}}{1}=10 \sqrt{2} \mathrm{~kg}
\end{aligned}
$$
\begin{aligned}
\overrightarrow{\mathrm{F}} & =6 \hat{\mathrm{i}}-8 \hat{\mathrm{j}}+10 \hat{\mathrm{k}} \\
|\overrightarrow{\mathrm{F}}| & =\sqrt{6^2+8^2+10^2}=10 \sqrt{2} \\
\mathrm{~m} & =\frac{|\overrightarrow{\mathrm{F}}|}{\mathrm{a}}=\frac{10 \sqrt{2}}{1}=10 \sqrt{2} \mathrm{~kg}
\end{aligned}
$$
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