A, B and C are the three forces each of magnitude 4N acting in the plane of paper as shown in figure. The point O lies in the same plane.

(i) Which force has the least moment about O? Give reason.

(ii) Which force has the greatest moment about O? Give reason.

(iii) Name the forces producing (a) clockwise, (b) anticlockwise moments.

(iv) What is the resultant torque about the point O?

(i)
We know that,

Moment of force = Force × Perpendicular distance

We can see from the given figure that vector C has least perpendicular distance from point O.

Hence, vector C will have least moment about O.

(ii)
We know that,

Moment of force = Force × Perpendicular distance

We can see from the given figure that vector A has greatest perpendicular distance from point O

Hence, vector A will have greatest moment about O.

(iii)
(a) Clockwise moments are produced by vectors A and B.

Reason : If turning effect on the body is clockwise then moment of force is called clockwise moment and it is taken as a negative value.

(b) Anticlockwise moment is produced by vector C.

Reason : If turning effect on the body is anticlockwise then moment of force is called anticlockwise moment and it is taken as a positive value.

(iv)
Sum of torques due to vectors A, B and C = Resultant torque about point O

$-(4 \times 0.9) - (4 \times 0.8) + (4 \times 0.6)Nm \\[0.5em] = -3.6 - 3.2 + 2.4 Nm \\[0.5em] = -4.4 Nm$

So, the resultant torque is 4.4Nm (clockwise direction).