Verified Solution • 2025–26 Session moderate

QJEEM22Ph4cd0: JEE Main 2022 Physics - Class 11 JEEM22Ph4cd0 Solution: Four spheres each of mass m from a square of side d (as shown…

Four spheres each of mass m from 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 :

JEE Main 2022 (Online) 27th June Evening Shift Physics - Gravitation Question 90 English

Multiple Choice Options

  • A −Gmd[(4+2)m+42M]- {{Gm} \over d}\left[ {(4 + \sqrt 2 )m + 4\sqrt 2 M} \right]
  • B −Gmd[(4+2)M+42m]- {{Gm} \over d}\left[ {(4 + \sqrt 2 )M + 4\sqrt 2 m} \right]
  • C −Gmd[3m2+42M]- {{Gm} \over d}\left[ {3{m^2} + 4\sqrt 2 M} \right]
  • D −Gmd[6m2+42M]- {{Gm} \over d}\left[ {6{m^2} + 4\sqrt 2 M} \right]

Step-by-Step Verified Solution

Total gravitational potential energy

=−{4GMmd/2+4Gm2d+2Gm22d}= - \left\{ {{{4GMm} \over {d/\sqrt 2 }} + {{4G{m^2}} \over d} + {{2G{m^2}} \over {\sqrt 2 d}}} \right\}

=−Gmd{M42+(4+2)m}= - {{Gm} \over d}\left\{ {M4\sqrt 2 + (4 + \sqrt 2 )m} \right\}

=−Gmd{42M+(4+2)m}= - {{Gm} \over d}\left\{ {4\sqrt 2 M + (4 + \sqrt 2 )m} \right\}

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring