A particle moves under the action of a force $\vec{F}=20 \hat{i}+15 \hat{j} \mathrm{~N}$ along a str

Question

A particle moves under the action of a force $\vec{F}=20 \hat{i}+15 \hat{j} \mathrm{~N}$ along a straight line $3 y+\alpha x=5$, where $\alpha$ is a constant. If the work done by the force $F$ is zero, then the value of $\alpha$ is

Professor PC Thomas Classes · Answer

The slope of the line is $\frac{d y}{d x}=-\frac{\alpha}{3}$ ∴ The displacement vector is $\vec{s}=3 x \hat{i}-\alpha x \hat{j}$ and the force vector is $\vec{F}=20 \hat{i}+15 \hat{j}$ Since $W=\vec{F} \cdot \vec{s}=0$, therefore, \ $ \begin{aligned} & (20 \hat{i}+15 \hat{j})(3 x \hat{i}-\alpha x \hat{j})=0 \ & 60-15 \alpha=0 \end{aligned} $ \ or $ \alpha=4 $