COMEDK · Physics · 9. Gravitation

A particle of mass 1 kg is kept on the surface of a uniform sphere of mass 20 kg and radius 1.0 m . The work to be done against the gravitational force between them to take the particle away from the sphere is

A \(0.5 \times 10^{-9} \mathrm{~J}\)
B \(1.334 \times 10^{-9} \mathrm{~J}\)
C \(2532 \times 10^{-9} \mathrm{~J}\)
D zero

Verified Solution

Answer & Solution

Correct Answer

(B) \(1.334 \times 10^{-9} \mathrm{~J}\)

Step-by-step Solution

Detailed explanation

Potential at the surface of earth, \(V=-\frac{G M}{R}\) \(\begin{aligned} & =-\frac{6.67 \times 10^{-11} \times 20}{1} \\ & =-1.334 \times 10^{-9} \mathrm{~J} / \mathrm{K} \end{aligned}\) i.e., \(1.334 \times 10^{-9} \mathrm{~J}\) work is done to bring a mass of 1 kg from…

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.

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