An object of mass m is raised from the surface of the earth to a height equal to the radius of the earth, that is, taken from a distance R to 2R from the centre of the earth. What is the gain in its potential energy ?

An object of mass m is raised from the surface of the earth to a heigh

1.	An object of mass m is raised from the surface of the earth to a height equal to the radius of the earth, that is, taken from a distance R to 2R from the centre of the earth. What is the gain in its potential energy ?
Answer» <html><body><p></p>Solution :<img src="https://doubtnut-static.s.llnwi.net/static/physics_images/KPK_AIO_PHY_XI_P1_C08_E04_032_S01.png" width="80%"/><br/>Potential energy of the <a href="https://interviewquestions.tuteehub.com/tag/object-11416" style="font-weight:bold;" target="_blank" title="Click to know more about OBJECT">OBJECT</a> at the surface of the earth = `-(<a href="https://interviewquestions.tuteehub.com/tag/gmm-2090431" style="font-weight:bold;" target="_blank" title="Click to know more about GMM">GMM</a>)/R` <br/> PE of the object at a height <a href="https://interviewquestions.tuteehub.com/tag/equal-446400" style="font-weight:bold;" target="_blank" title="Click to know more about EQUAL">EQUAL</a> to the radiusof the earth `=-(GMm)/(<a href="https://interviewquestions.tuteehub.com/tag/2r-300472" style="font-weight:bold;" target="_blank" title="Click to know more about 2R">2R</a>)` <br/> `:.` Gain in PE of the object <br/> `=(-GMm)/(2R) -(-(GMm)/R)` <br/> `=(-GMm+2GMm)/(2R) = +(GMm)/(2R)`<br/> `= (gR^2xxm)/(2R) = 1/2 mgR "" ( :. g = (GM)/(R^2))`</body></html>