Q. If a particle is compelled to move on a given smooth plane curve under the action of given forces in the plane $\overrightarrow{\mathbf{F}} = x\widehat{\mathbf{i}} + y\widehat{\mathbf{j}}$, then
A) $\overrightarrow{\mathbf{F}}\mathbf{.}\overrightarrow{\mathbf{dr}} = xdx + ydy$
B) $\int_{}^{}\overrightarrow{\mathbf{F}}.\overrightarrow{\mathbf{dr}} \neq \frac{1}{2}mv^{2}$
C) $\overrightarrow{\mathbf{F}}\mathbf{.}\overrightarrow{\mathbf{dr}} \neq xdx + ydy$
D) $\frac{1}{2}mv^{2} \neq \int_{}^{}{(xdx + ydy)}$
Explanation
(a) $\overrightarrow{\mathbf{F}}\mathbf{.}d\overrightarrow{\mathbf{F}} = \left( x\widehat{\mathbf{i}} + y\widehat{\mathbf{j}} \right).(dx\widehat{\mathbf{i}} + dy\widehat{\mathbf{j}})$
$= xdx + ydy$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.