If one wants to remove all the mass of the earth to infinity in order to break it up completely. The amount of energy that needs to be supplied will be \(\frac{x}{5}\, \frac{ GM ^{2}}{ R }\) where \(x\) is \(\quad\,..........\) (Round off to the Nearest Integer) (\(M\) is the mass of earth, \(R\) is the radius of earth, \(G\) is the gravitational constant)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.