TS EAMCET · Physics · Gravitation

Three particles, each of mass $M$ , situated at the vertices of an equilateral triangle of side length $L$ . The only forces acting on the particles are their mutual gravitational forces. It is desired that each particle moves in a circle while maintaining the original separation $L$ . The initial speed that should be given to each particle is

A $\sqrt{\frac{2 GM}{L}}$
B $\sqrt{\frac{GM}{2 L}}$
C $\sqrt{\frac{GM}{L}}$
D $\sqrt{\frac{3 GM}{L}}$

Verified Solution

Answer & Solution

Correct Answer

(C) $\sqrt{\frac{GM}{L}}$

Step-by-step Solution

Detailed explanation

As the particles move under gravitational influence, the gravitational force will provide the centripetal force required. Gravitational force between two bodies of masses m1 and m2 separated by distance d is given by, Gm1m2d2, where G is the universal gravitational constant. Net…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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