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 moves with unifrom speed (a) Show that the forces are coplaner.
(b) Show that the torque acting on the body about any point due to these three forces is zero .

Explanation

(a) As the is moving with unifrom speed its acceleration ` a = 0 `
` :. vec (F_(1)) + vec (F_(2)) + vec (F_(3)) = 0 `
The three forces are passing through a point `P` as shown in
If ` vec(F_(1)), + vec (F_(2)) ` lie in one plane say `A` , their resultant lies in plane `A`
Since ` vec(F_(3)) = - (vec(F_(1)) + vec(F_(2)))` ,therefore `vec(F_(3)` must also lin in plane A Hence
`vec (F_(1)) , vec(F_(2)) vec (F_(3))` are coplaner forces
(b) Since all the forces pass through same point `P` therefore, torque acting on the body about `P` due to the these three forces is zero . About any other
point say o torque `= vec(OP) xx (vec(F_(1)) + vec(F_(2))vec (F_(3)))`
As `vec(F_(1)) + vec(F_(2)) + vec(F_(3)) = 0` therefore , torque about point O = zero
.