P, Q and R are the three forces, each of magnitude 6 N acting in the plane of paper as shown in Fig. The point O lies in the same plane. (i) Which force has the least moment about O?

Question

P, Q and R are the three forces, each of magnitude 6 N acting in the plane of paper as shown in Fig. The point O lies in the same plane.

shaalaa.com · Accepted Answer

Since all three forces have the same magnitude, the moment depends on the perpendicular distance from O to the line of action of the force.

Moment of a force = Force × perpendicular distance

(i) Force R has the least moment about O.

τR = 6 × 0.6

= 3.6 N m

(ii) Force P has the greatest moment about O.

τP = 6 × 0.9

= 5.4 N m

Force Q produces:

τQ = 6 × 0.8

= 4.8 N m

The moment is calculated using τ = F × d, where ddd is the perpendicular distance from O to the line of action of the force.

(iii) (a) P and Q produce clockwise moments.

(iii) (b) R produces an anticlockwise moment.

(iv) Resultant torque about O:

Clockwise torque = 5.4 + 4.8

= 10.2 N m

Anticlockwise torque = 3.6 N m

Resultant torque = 10.2 − 3.6

= 6.6 N m

Therefore, the resultant torque about point O is 6.6 N m clockwise.