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प्रश्न
The vector sum of a system of non-collinear forces acting on a rigid body is given to be non-zero. If the vector sum of all the torques due to the system of forces about a certain point is found to be zero, does this mean that it is necessarily zero about any arbitrary point?
उत्तर
The vector sum of all torques due to forces at a point is 0.
Let us assume that τ be the torque about a point P
Then `τ = τ_1 + τ_2 + .......... + τ_n`
= `sum_(i - 1)^n vecr_i xx vecF_i` = 0 ....(As per question)
Now torque about any other point say A will be given by
`sum_(i = 1)^n (vecr_i - a) xx vecF_i sum_(i = 1)^n vecr_i xx vecF_i - a sum_(i = 1)^n vecF_i`
Since a and `sum_(i = 1)^n vecF_i` are not equal to zero. Thus the sum of all torques about any arbitrary point is not 0 necessarily.
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