Q. 95.0( 2 Votes )

If several forces act on a particle, the total torque on the particle may be obtained by first finding the resultant force and then taking torque of this resultant. Prove this. Is this result valid for the forces acting on different particles of a body in such a way that their lines of action intersect at a common point?

Class 11th HC Verma - Concepts of Physics Part 1 10. Rotational Mechanics

Answer :

Let us assume there are n number of forces acting on H. so, the torque will be

Hence, the statement is proved.

This statement is valid till there exists a common point of intersection.

Let us assume there exists n number of forces having a common point of intersection P. The forces Are applied at particles A, B, C… We are going to find the torque about the point O.

In the diagram A is connected by R₁. Using vector summation we can write

So, for the i^th particle

Torque,

But

as the angle between them is π.

So,

Hence, the statement is valid till it has a common point of intersection.

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