Q. 355.0( 2 Votes )

# Six point masses of mass m each are at the vertices of a regular hexagon of side l. Calculate the force on any of the masses.

Answer :

Given

Side of hexagon = l

The force on the masses will be the resultant of the forces of all the other masses. Let the masses be m each. Now the distance AC is given by the parallelogram law i.e.

Due to symmetry we have AC = AE =

Now, for AD we have

Now the force on mass at A due to b is

Also

The force on mass A due to C is

Also due to symmetry, we have

The force on mass at A due to mass at D is

Now, the forces F_{ae} and F_{ac} make equal angles with the direction AD viz. 30°, and therefore by parallelogram law of vector addition their resultant is along AD and therefore the magnitude of the resultant,

Similarly, F_{ab} and F_{af} also make equal angles with AD viz. 60° and therefore they are also along AD and

Therefore, the net force on mass at A will be

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