Calculate the net torque on the system about the point O as shown in figure if F1=11N,F2=9N,F3=10N,a=10cm and b=20cm (All the forces are along the tangents)
A
2.2Nm out of the plane
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B
3.0Nm into the plane
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C
2.2Nm into the plane
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D
3.0Nm out of the plane
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Solution
The correct option is B3.0Nm into the plane
As we know, →τ=→r×→F=r⊥F
Torque because of force F1 at origin, →τ1=r⊥−→F1=b.F1=0.2×11=2.2Nm (direction into the plane)
Torque because of force F2 at origin, →τ2=r⊥.F2=b.F2=0.2×9=1.8Nm (direction into the plane)
Torque because of force F3 at origin, →τ3=r⊥.F3=a.F3=0.1×10=1Nm (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)=3.0Nm (into the plane)