Q9 of 35 Page 55

100 coplanar forces each equal to 10N act on a body. Each force makes an angle π/50 with the preceding force. What is the resultant of the forces?

Now the total angle covered by the 100 coplanar forces of 10 N each is given by:

Total Angle Covered =


The head of the last force vector joins the tail of the first vector. Thus this makes a regular polygon of 100 sides. For a regular polygon (that is a polygon having all sides equal) we will always have an equal and opposite pair of force.


For Example, consider a square as shown below:


This is a regular polygon of 4 sides having same force magnitude. Thus they would cancel each other.


Thus,



Now, consider a regular hexagon as shown below.



This is a regular polygon with six sides.


All forces have one force that is equal and opposite of it. Hence,


Similarly, our regular polygon of 100 sides also has .


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