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

Question

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

Infinity Learn · Accepted Answer

Gravitational potential energy at any point at a distance r from the centre of the earth $$isU=$$−GMmrwhere M and m be masses of the earth and the body respectively.At the surface of the earth, r $$=$$ R∴   $$Ui=GMmRAt$$ a height h from the surface.$$r=R+h=R+2R$$    ∵$$h=2RGiven=$$ $$3R$$∴   $$Uf=GMm3RChange$$ in potential energy,Δ$$U=Uf$$−Ui $$=$$−$$GMm3R$$−−GMmR $$=GMmR1$$−$$13=23GMmR$$ $$=23mgR$$              ∵$$g=GMR2$$

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

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