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A body under the action of a force $\mathbf{F}=6 \hat{\mathbf{i}}-8 \hat{\mathbf{j}}+10 \hat{\mathbf{k}}$, 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:
$10 \sqrt{2} \mathrm{~kg}$
Given, $\mathbf{F}=6 \hat{\mathbf{i}}-8 \hat{\mathbf{j}}+10 \hat{\mathbf{k}}$
$$
\begin{aligned}
a &=1 \mathrm{~m} / \mathrm{s}^{2} \\
|\mathbf{F}| &=\sqrt{6^{2}+(-8)^{2}+10^{2}} \\
&=\sqrt{200} \\
\Rightarrow \quad|\mathbf{F}| &=10 \sqrt{2} \mathrm{~N} \\
\Rightarrow \quad m a &=10 \sqrt{2} \\
\Rightarrow \quad m &=\frac{10 \sqrt{2}}{a} \\
&=\frac{10 \sqrt{2}}{1} \\
&=10 \sqrt{2} \mathrm{~kg}
\end{aligned}
$$
$$
\begin{aligned}
a &=1 \mathrm{~m} / \mathrm{s}^{2} \\
|\mathbf{F}| &=\sqrt{6^{2}+(-8)^{2}+10^{2}} \\
&=\sqrt{200} \\
\Rightarrow \quad|\mathbf{F}| &=10 \sqrt{2} \mathrm{~N} \\
\Rightarrow \quad m a &=10 \sqrt{2} \\
\Rightarrow \quad m &=\frac{10 \sqrt{2}}{a} \\
&=\frac{10 \sqrt{2}}{1} \\
&=10 \sqrt{2} \mathrm{~kg}
\end{aligned}
$$
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