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Question

Calculate the net torque on the system about the point O as shown in figure if F1=11 N,F2=9 N,F3=10 N,a=10 cm and b=20 cm (All the forces are along the tangents)


A
2.2 Nm out of the plane
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B
3.0 Nm into the plane
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C
2.2 Nm into the plane
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D
3.0 Nm out of the plane
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Solution

The correct option is B 3.0 Nm into the plane

As we know, τ=r×F=rF
Torque because of force F1 at origin,
τ1=rF1=b.F1=0.2×11=2.2 Nm (direction into the plane)

Torque because of force F2 at origin,
τ2=r.F2=b.F2=0.2×9=1.8 Nm (direction into the plane)

Torque because of force F3 at origin,
τ3=r.F3=a.F3=0.1×10=1 Nm (direction out of the plane)

Hence net torque (assume direction of torque into the plane as positive)
τ=τ1+τ2+τ3
i.e τ=2.2+1.8+(1)=3.0 Nm (into the plane)

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