There are three forces `F_(1) , F_(2)` and `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.

Explanation

As the body is moving with uniform speed (velocity) its acceleration a = 0
`therefore` The sum of the forces is zero.

Let `F_(1) , F_(2), F_(3)` be the three forces passing through a point . Let `F_(1)` and `F_(2)` be in the plane A (one can always draw a plane having two intersecting lines such that the two lines lie on the plane ) . Then `F_(1) + F_(2)` must be in the plane A .
Since `F_(3) = -(F_(1) + F_(2)) , F_(3)` is also in the plane A .
(b) Consider the torque of the forces about P . Since all the forces pass through P , the torque is zero .Now , consider torque about another point O. Then torque about O is
Torque = `OP xx (F_(1) + F_(2) + F_(3))`
Since , `F_(1) + F_(2) + F_(3) = 0` , torque = 0 .