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Question

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

A
10^i+14^j9^k
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B
14^i+5^j9^k
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C
14^i9^j+10^k
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D
14^i+10^j9^k
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Solution

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

Let the position vector of (1,1,0) and (0,1,2) w.r.t point (1,0,1) be r1 and r2 .
Therefore, r1=(^i+^j)(^i+^k)=2^i+^j^k
r2=(^j+2^k)(^i+^k)=^i+^j+^k
Then, net torque is given by
τ=r1×F1+r2×F2

Now, r1×F1=∣ ∣ ∣^i^j^k211256∣ ∣ ∣=11^i+10^j12^k
and
r2×F2=∣ ∣ ∣^i^j^k111121∣ ∣ ∣=3^i+3^k
So, resultant torque =(11^i+10^j12^k)+(3^i+3^k)
=14^i+10^j9^k N-m


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