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Question

Two forces F1=2^i5^j6^k and F2=^i+2^j^k are acting on a body at a point (1,1,0) and (0,1,2) respectively. Find the torque acting on the body about the point (1,0,1).

A
14^i+10^j9^k
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B
11^i+10^j12^k
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C
3^i+3^k
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D
14^i10^j9^k
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Solution

The correct option is A 14^i+10^j9^k

From the diagram,
r1=(1(1))^i+(10)^j+(01)^k
r1=2^i+^j^k........(I)

r2=(0(1))^i+(10)^j+(21)^k
r2=^i+^j+^k.....(II)

As we know, τ=r×F
τ1=r1×F1
τ1=∣ ∣ ∣^i^j^k211256∣ ∣ ∣
τ1=i(65)j(12+2)+^k(102)
=11^i+10^j12^k
And
τ2=r2×F2
τ=∣ ∣ ∣^i^j^k111121∣ ∣ ∣
τ2=^i(12)^j(1+1)+^k(2+1)
τ2=3^i+3^k

Therefore, net torque about point (1,0,1) is
τ=τ1+τ2
τ=11^i+10^j12^k3^i+3^k
τ=14^i+10^j9^k

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