Question

A particle is acted upon by the constant forces $4\hat{i}+\hat{j}-3\hat{k}$ and $3\hat{i}+\hat{j}-\hat{k}$ which displace it from a point $\hat{i}+2\hat{j}+3\hat{k}$ to $5\hat{i}+4\hat{j}+\hat{k}$. The work done is standard unit by the forces is given by

• A. $25$
• B. $30$
• C. $40$
• D. $15$

Answer 1

The correct option is C $40$

Total force $\overline{F}={\overline{F}}_{{}_1}+{\overline{F}}_{{}_2}$

$=7\hat{i}+2\hat{j}-4\hat{k}$
Displacement $\overline{d}={\overline{d}}_{{}_2}-{\overline{d}}_{{}_1}=(5-1)\hat{i}+(4-2)\hat{j}+(\hat{k}-3)\hat{k}$

$\therefore$ Work done $=\overline{F}\cdot \overline{d}=28+4+8=40$