A force $(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}) \mathrm{N}$ acts on a body, which is…
A force $(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}) \mathrm{N}$ acts on a body, which is initially at rest. At the end of $20 \mathrm{~s}$ the velocity of the body is $(4 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}) \mathrm{ms}^{-1}$, then the mass of the body is
$8\ kg$
$10\ kg$
$5\ kg$
$4.5\ kg$
Solution
$|\mathrm{F}|=F=\sqrt{4+1+1}=\sqrt{6}$
$v=\sqrt{16+4+4}=\sqrt{24}$
Now, $F=\frac{d p}{d t}=m\left(\frac{v-u}{t}\right)$
where, $\mathrm{m}=$ mass of body
$\Rightarrow \quad \sqrt{6}=m\left(\frac{\sqrt{24}-0}{20}\right) \Rightarrow m=\frac{\sqrt{6} \times 20}{\sqrt{24}}=10 \mathrm{~kg}$