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There are three forces $\vec {F_1}$, $\vec {F_2}$ and $\vec {F_3}$ acting on a body, all acting on a point $P$ on the body. The body is found to move with uniform speed.
$(a)$ Show that the forces are coplanar.
$(b)$ Show that the torque acting on the body about any point due to these three forces is zero.
Solution
As shown in figure, three forces $\mathrm{F}_{1}, \mathrm{~F}_{2}, \mathrm{~F}_{3}$ act at point $\mathrm{P}$ on body.
$(a)$ Figure shows that forces are in same plane that is forces are coplaner. Body moves with constant uniform speed (velocity).
$\therefore a =0$
$\mathrm{~F} =m a$
$=m(c)$
$=0$
$\therefore \overrightarrow{\mathrm{F}}_{1} +\overrightarrow{\mathrm{F}}_{2}+\overrightarrow{\mathrm{F}}_{3}=0$
$(b)$ Calculating torque of these forces about point$ P$. As forces passes through$ P$ torque about point $\mathrm{P}$ is zero.
