Question 153: Gravitation

Question

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 :

Accepted Answer

Total gravitational potential energy
$$ =  - \left\{ {{{4GMm} \over {d/\sqrt 2 }} + {{4G{m^2}} \over d} + {{2G{m^2}} \over {\sqrt 2 d}}} \right\}$$
$$ =  - {{Gm} \over d}\left\{ {M4\sqrt 2  + (4 + \sqrt 2 )m} \right\}$$
$$ =  - {{Gm} \over d}\left\{ {4\sqrt 2 M + (4 + \sqrt 2 )m} \right\}$$

Answer

$$ - {{Gm} \over d}\left[ {(4 + \sqrt 2 )m + 4\sqrt 2 M} \right]$$

Answer

$$ - {{Gm} \over d}\left[ {(4 + \sqrt 2 )M + 4\sqrt 2 m} \right]$$

Answer

$$ - {{Gm} \over d}\left[ {3{m^2} + 4\sqrt 2 M} \right]$$

Answer

$$ - {{Gm} \over d}\left[ {6{m^2} + 4\sqrt 2 M} \right]$$

Gravitation

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 :

Choose the correct answer: