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If g is the acceleration due to gravity on the surface of the earth, the gain in potential energy of an object of mass m raised from the earth's surface to a height equal to the radius R of the earth is |
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Answer» Solution :Gravitational potential ENERGY of an object of mass ms at any point at a distance r from the centre of the earth is `U=-(GMm)/(r )` Where M is the mass of the earth. At the surface of the earth, r=R `:. U_(1)=-(GMm)/(R )=-mgR(.: g=(GM)/(R^(2)))""`..(i) At a height R from the surface of the earth, r=2R `:. U_(2)=-(GMm)/(2R )=-(mgR)/(2)""` ....(ii) Gain in potential energy, `DeltaU=U_(2)-U_(1)` `DeltaU=-(mgR)/(2)-(-mgR)`(Using (i)and (ii)) `=(mgR )/(2)`. |
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