JEE Mains · Physics · STD 11 - 7. gravitation
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
- A \(-\frac{ Gm }{ d }[(4+\sqrt{2}) m +4 \sqrt{2} M]\)
- B \(-\frac{ Gm }{ d }[(4+\sqrt{2}) M +4 \sqrt{2} M ]\)
- C \(-\frac{ Gm }{ d }\left[3 m ^{2}+4 \sqrt{2} M \right]\)
- D \(-\frac{ Gm }{ d }\left[6 m ^{2}+4 \sqrt{2 M }\right]\)
Answer & Solution
Correct Answer
(A) \(-\frac{ Gm }{ d }[(4+\sqrt{2}) m +4 \sqrt{2} M]\)
Step-by-step Solution
Detailed explanation
\(-\frac{ Gm ^{2}}{ d } \times 4-\frac{ Gm ^{2}}{\sqrt{2} d } \times 2-\frac{ GMm }{ d } \times 4 \sqrt{2}\) \(-\frac{ Gm }{ d }[(4+\sqrt{2}) m +4 \sqrt{2} M ]\)
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