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4 identicle bodies of mass m are located at vertices of square of side l they revolve under the effect of mutual gravitational force in circle circumscribing the square then the speed of each body will be
Asked by shivanipanchal6883 | 05 Jan, 2023, 02:44: PM
Figure shows system that consists of 4 partcles of mass m positioned at the vertex of square of side l .

Each mass is attracted along sides by force FS and also along diagonal by force FD .

Force FS =
Force FD =
where G is universal gravitational constant.

Forces acting on sides gives resultant along diagonal .

Hence net resultant force Fnet acting on each mass along diagonal is

Fnet = √2 FS + FD =
If above force is acting as centripetal force for the masses to rotate along circle
that is circumscribing the square , then speed v of each mass is determined as follows

where R =   is radius of circle

After simplification of above expression, we get

Answered by Thiyagarajan K | 05 Jan, 2023, 05:32: PM

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