When a force $\mathbf{F}$ given by $\mathbf{F}=(6 \hat{\mathbf{i}}-18 \hat{\mathbf{j}}+10 \hat{\mathbf{k}})…
When a force $\mathbf{F}$ given by $\mathbf{F}=(6 \hat{\mathbf{i}}-18 \hat{\mathbf{j}}+10 \hat{\mathbf{k}}) \mathrm{N}$ acts on a body, it imparts an acceleration of $8 \mathrm{~ms}^{-2}$. Then, find the mass of the body.
$\frac{\sqrt{115}}{4} \mathrm{~kg}$
$10 \sqrt{2} \mathrm{~kg}$
$\frac{\sqrt{115}}{2} \mathrm{~kg}$
$\frac{115}{2} \mathrm{~kg}$
Solution
Given that, force vector,
$
\mathbf{F}=(6 \hat{\mathbf{i}}-18 \hat{\mathbf{j}}+10 \hat{\mathbf{k}}) \mathrm{N}
$
Magnitude of force,
$
\begin{aligned}
F & =|\mathbf{F}|=\sqrt{(6)^2+(-18)^2+(10)^2} \\
& =\sqrt{460} \mathrm{~N}
\end{aligned}
$
Acceleration, $a=8 \mathrm{~m} / \mathrm{s}^2$
By Newton's law of motion,
$
\begin{array}{ll}
& F=m a \\
\Rightarrow & m=\frac{F}{a}
\end{array}
$
By substituting the values, we get
Mass of body, $m=\frac{\sqrt{460}}{8}=\frac{\sqrt{115}}{4} \mathrm{~kg}$