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A particle of mass 10 g is kept on the surface of a uniform sphere of mass 100 kg and radius 10 cm. Find the work to be done against the gravitational force between them to take the particle far away from the sphere. (You may take G=6.67×10⁻¹¹ N m²/kg²)

Asked in AIEEE 2005 · Self energy and binding energy

• (1) 6.67×10⁻⁹ J
• (2) 6.67×10⁻¹⁰ J
• (3) 13.34×10⁻¹⁰ J
• (4) 3.33×10⁻¹⁰ J

Step-by-step solution

Why the other options are wrong

• (1) Ten times too big, which is what R=1 cm would give; the radius must go in as 0.1 m.
• (3) Double the correct value, from using (2GMm)/R, the escape-energy expression, instead of the binding energy (GMm)/R.
• (4) Half the correct value, from carrying the 1/2 of 1/2mv² into the potential-energy term as well.

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