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JEE Main202227 Jun 2022Evening ShiftPhysicsGravitationActual

Four spheres each of mass m form a square of side d (as shown in figure). A fifth sphere of mass M is situated at the centre of square. The total gravitational potential energy of the system is

Options

  1. A- G m d 4 + 2 m + 4 2 M
  2. B- G m d 4 + 2 M + 4 2 m
  3. C- G m d 3 m 2 + 4 2 M
  4. D- G m d 6 m 2 + 4 2 M

Correct answer

A. - G m d 4 + 2 m + 4 2 M

Step-by-step solution

The total gravitational potential energy of the system is U s y s t e m = U 12 + U 23 + U 34 + U 41 + U 13 + U 24 + U 15 + U 25 + U 35 + U 45 = - 4 G m m d - 2 G m m d 2 - 4 2 G M m d = - 4 + 2 G m 2 d - 4 2 G M m d = - G m d 4 + 2 m + 4 2 M

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