Ncert Exercises & Solutions

Q. 19 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 an arbitrary point?

Hint: Recall the concept of torque on a rigid body.

Step 1: Find the torque about any other points and interpret the answer.

Given,
$\sum_{j} F_{i} \neq 0$ $\sum_{j} F_{i} \neq 0$
The sum of torques about a certain point O. $\sum_{i} r_{i} \times F_{i} = 0$ $\sum_{i} r_{i} \times F_{i} = 0$
The sum of torques about any other O'

$\sum_{i} (r_{i} - a) \times F_{i} = \sum_{i} r_{i} \times F_{i} - a \times \sum_{i} F_{i}$ $\sum_{i} (r_{i} - a) \times F_{i} = \sum_{i} r_{i} \times F_{i} - a \times \sum_{i} F_{i}$

Here, the second term need not vanish.

Therefore, the sum of all the torques about any arbitrary point need not zero necessarily.

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