Q: There are three forces F_{1} , F_{2} , F_{3} acting on a body, all acting on a point on the body. The body is found to move with uniform speed.

(i) Show that the forces are coplanar.

(ii) Show that the torque acting on the body about any point due to these three forces is zero.

Sol: As body is moving with uniform speed , $\vec{a} = 0 $ and hence $\vec{F} = 0$

$\displaystyle \vec{F_1} + \vec{F_2} + \vec{F_3} = 0 $

three forces F_{1} , F_{2} , F_{3} acting on a body, all acting on a point . Suppose F_{1} and F_{2} is in a Plane A ,hence $\displaystyle \vec{F_1} + \vec{F_2} $ be in plane A

Therefore $\displaystyle \vec{F_3} = – (\vec{F_1} + \vec{F_2} ) $ is also in Plane A

Hence Co-planar .

since $\displaystyle \vec{F_1} + \vec{F_2} + \vec{F_3} = 0 $

Hence Torque about any point P will be

$\displaystyle \vec{OP} \times\vec{F_1} + \vec{F_2} + \vec{F_3} = 0 $