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Show that moment of a couple does not depend on the point about which you take the moments.

Answer» <html><body><p></p>Solution :<img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/NCERT_GUJ_PHY_XI_P1_C07_SLV_007_S01.png" width="80%"/> <br/> Consider a couple as shown in Fig. 7.22 <a href="https://interviewquestions.tuteehub.com/tag/acting-269" style="font-weight:bold;" target="_blank" title="Click to know more about ACTING">ACTING</a> on a rigid body. The forces `F and -F` act respectively at points B and A. These points have position <a href="https://interviewquestions.tuteehub.com/tag/vectors-14090" style="font-weight:bold;" target="_blank" title="Click to know more about VECTORS">VECTORS</a> `r_(1) and r_(2)` with respect to origin O. Let us take the <a href="https://interviewquestions.tuteehub.com/tag/moments-1100584" style="font-weight:bold;" target="_blank" title="Click to know more about MOMENTS">MOMENTS</a> of the forces about the origin. <br/> The moment of the couple = sum of the moments of the two forces making the couple <br/> `=r_(1)<a href="https://interviewquestions.tuteehub.com/tag/xx-747671" style="font-weight:bold;" target="_blank" title="Click to know more about XX">XX</a>(-F)+r_(2)xxF` <br/> `=r_(2)xxF-r_(1)xxF` <br/> `=(r_(2)-r_(1))xxF` <br/> But `r_(1)+AB=r_(2)`, and hence `AB=r_(2)-r_(1)`. <br/> The moment of the couple, therefore, is `AB × F`. <br/> Clearly this is independent of the origin, the <a href="https://interviewquestions.tuteehub.com/tag/point-1157106" style="font-weight:bold;" target="_blank" title="Click to know more about POINT">POINT</a> about which we took the moments of the forces.</body></html>


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