A body is in translational equilibrium under the action of coplanar forces. If the torque of these forces is zero about a point, is it necessary that it will also be zero about any other point?

Open in App

Solution

$Yes, if the torque due to forces in translation equillibrium is zero about a point, it will be zero about other point in the plane .$

$Let us consider a planner lamina of some mass, acted upon by forces \vec{F_{1}}, \vec{F_{2}}, . . . \vec{F_{i}}, etc . Let a force \vec{F_{i}} act on a i^{th} particle and torque due to \vec{F_{i}} be zero at a point Q . Since the body is in translation equillibrium, we have : Σ \vec{F_{i}} = 0 . . . (1) Again, torque about P is zero . Therefore, we have : Σ (\vec{r_{p i}} \times \vec{F_{i}}) = 0 . . . (2) Now, torque about point Q will be : Σ {\vec{r}}_{Qi} \times \vec{F_{i}} = Σ ({\vec{r}}_{Q P} + {\vec{r}}_{P i}) \times \vec{F_{i}} [From fig . 13] = Σ ({\vec{r}}_{Q P} \times \vec{F_{i}} + \vec{r_{P i}} \times \vec{F_{i}}) = Σ \vec{r_{Q P}} \times \vec{F_{i}} + Σ \vec{r_{P i}} \times \vec{F_{i}} = \vec{r_{QP}} \times Σ \vec{F_{i}} + 0 [From (2)] = \vec{r_{Q P}} \times 0 [From (1)] = 0 Thus, \vec{F} is zero about any other point Q .$

Suggest Corrections

Similar questions

Q. Statement I: Torque of pseudo force about any point lying on the rigid body is always zero.
Statement II: Torque of pseudo force about the centre of mass of the rigid body is always zero.

If a body is rotating about a given Axis and a Force is applied at any point on that body along any random direction, what can we say about the torque of this force about any point lying on its Axis of rotation?

Q. Assertion :Moment of concurrent forces about any point is constant. Reason: If vector sum of all the concurrent forces is zero, then moment of all the forces about any point is also zero.

Q. Which of the following conditions are necessary for a rigid body to be in mechanical equilibrium?
Condition 1: Net external force acting on body is zero.
Condition 2: Net external torque acting on body is zero.
Condition 3: Internal forces and torque due to internal forces must be absent.

Q. For rotational equilibrium of a rigid body, it is essential that net torque about the axis of rotation must be zero.

Join BYJU'S Learning Program