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An object of mass 1 kg is taken to a height from the surface of the earth which is equal to three times the radius of the earth. The gain in potential energy of the object will be [take g=10 m s⁻² and radius of earth =6400 km]

Asked in JEE Main 29th July 2nd Shift 2022 · Potential energy of a system

• (1) 48 MJ
• (2) 24 MJ
• (3) 36 MJ
• (4) 12 MJ

Step-by-step solution

Why the other options are wrong

• (2) Half the correct value, which is what a radius of 3200 km would give.
• (3) Taking the final distance as 3R instead of 4R gives 2/3mgR=42.7 MJ, not this. This option is 9/(16)mgR, and no single consistent slip produces that fraction; it is a filler distractor sitting between 24 and 48 MJ.
• (4) A quarter of the right answer; the fraction 3/4 has been replaced by 3/(16), as if R were halved twice.

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