• # question_answer 19) Force acting on a particle is$\left( 2\widehat{i}+3\widehat{j} \right)N$. Work one by this force is zero, when a particle is moved on the line$3y+kx=5$. Here value of k is- A) 2                                 B) 4C) 6                                 D) 8

Force is parallel to a line $y=\frac{3}{2}\,\,x\,\,+\,\,c$ The equation of given line can be written as $y=-\frac{k}{3}\,x\,\,+\,\,\frac{5}{3}$ Work done will be zero, when force is perpendicular to the displacement i.e., the above two lines are perpendicular or ${{m}_{1}}{{m}_{2}}=-1$ or $\left( \frac{3}{2} \right)\left( -\frac{k}{3} \right)\,\,=\,\,-1$ $k=2$