\(A\) force \(\mathbf{F}=(5 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}) \mathrm{N}\) acts on a body and produces a…
\(A\) force \(\mathbf{F}=(5 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}) \mathrm{N}\) acts on a body and produces a displacement \(s=(6 \hat{\mathbf{i}}-5 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}) \mathrm{m}\). The work done by the force is
\(10 \mathrm{~J}\)
\(20 \mathrm{~J}\)
\(30 \mathrm{~J}\)
\(40 \mathrm{~J}\)
Solution
Force applied on the body,
\(\begin{aligned}
\mathbf{F} & =(5 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}) \mathrm{N} \\
\text {Displacement, } \mathbf{s} & =(6 \hat{\mathbf{i}}-5 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}) \mathrm{m} \\
\therefore \text { Work done, } W & =\mathbf{F} \cdot \mathbf{s}=(5 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}) \cdot(6 \hat{\mathbf{i}}-5 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}) \\
& =30-20+0=10 \mathrm{~J}
\end{aligned}\)