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A body of mass m is taken from the earth's surface to the height equal to twice the radius R of the earth. The change in potential energy of body will be

Asked in NEET 2013 · Work done and change in potential energy

Answer: (4) 2/3mgR

Step-by-step solution

Potential energy at distance r from the centre is U=-(GMm)/r.

At the surface, r=R and Uᵢ=-(GMm)/R.

At height 2R, r=R+2R=3R, so U_f=-(GMm)/(3R).

Δ U=U_f-Uᵢ=(GMm)/R(1-1/3)=2/3(GMm)/R.

Using GM=gR², Δ U=2/3mgR.

Why the other options are wrong

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