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The acceleration due to gravity on the surface of the earth is g. If a body of mass m is raised from the surface of the earth to a height equal to the radius R of the earth, then the gain in its potential energy is given byA. mgRB. 2 mgRC. `(1)/(2) mgR`D. `(1)/(4)mgR` |
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Answer» Correct Answer - C P.E. on the surface `=-(GMm)/(R )` P.E. at a height `h =R =-(GMm)/(R+R)` `therefore` Gain in P.E. `=-(GMm)/(2R)+(GMm)/(R )=(GMm)/(2R)` But `GM=gR^(2)therefore` Gain `=(gR^(2)m)/(2R)=(1)/(2)gmR` |
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