Q34 of 42 Page 35

There are three forces F1, F2 and F3 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.


(a)We know force is a vector quantity. From the theory of planes, we know that two intersecting lines form a plane.


Let these lines be F1 and F2. This means that the vector sum, F1 + F2 is also on this plane.


As the body is moving with uniform speed, the acceleration is zero. So the net of all forces is zero.


F1 + F2 + F3 =0


So, F3 = - (F1 + F2)


This means even F3 lies on the same plane as F1 and F2.


Thus the forces are coplanar.


(b) As the sum of all forces are zero, the net torque in any direction is zero. For example, torque about “O” is


Τ = OP x (F1 + F2 + F3)


Τ = 0 as (F1 + F2 + F3)=0


Hence, torque acting about any point is also zero.


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