AIIMS2018Physics-Gravitation

AIIMS 2018 Physics Gravitational Forces MCQ Question

Type: MCQ-conceptual-Medium-Class 11

Six stars of equal mass are moving about the centre of mass of the system such that they are always on the vertices of a regular hexagon of side length aa. Their common time period will be

A

4πa3Gm4\pi\sqrt{\frac{a^3}{Gm}}

B

2π43a3Gm(53+4)2\pi\sqrt{\frac{4\sqrt{3}a^3}{Gm(5\sqrt{3} + 4)}}

C

4π3a3Gm4\pi\sqrt{\frac{3a^3}{Gm}}

D

None of these.

Correct Answer

Option B

Detailed Explanation

Option B is correct because it accurately represents the derived period TT of the system based on the gravitational interactions outlined in the problem, specifically incorporating the factors derived from the forces F1,F2,F_1, F_2, and F3F_3. The other options do not align with the derived formula for TT, which is essential for understanding the oscillatory motion of the system under the influence of gravitational forces. By analyzing the relationships between the forces and their respective magnitudes, students can appreciate how gravitational interactions dictate the dynamics of the system.

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