Derive an expression for the gravitational potential energy of a body of mass 'm' raised to a height 'h' above the earth's surface.

Derive an expression for the gravitational potential energy of a body

1.	Derive an expression for the gravitational potential energy of a body of mass 'm' raised to a height 'h' above the earth's surface.
Answer» <html><body><p></p><a href="https://interviewquestions.tuteehub.com/tag/solution-25781" style="font-weight:bold;" target="_blank" title="Click to know more about SOLUTION">SOLUTION</a> :The gravitational potential energy (U) at some height h is equal to the aount of <a href="https://interviewquestions.tuteehub.com/tag/work-20377" style="font-weight:bold;" target="_blank" title="Click to know more about WORK">WORK</a> required to take the object from the <a href="https://interviewquestions.tuteehub.com/tag/ground-1013213" style="font-weight:bold;" target="_blank" title="Click to know more about GROUND">GROUND</a> to that height h. <br/> `U=intvecF_(a),dvecr=underset(0)overset(h)int\|vecF_(a)\|\|dvecr\|costheta` <br/> If the <a href="https://interviewquestions.tuteehub.com/tag/displacement-956081" style="font-weight:bold;" target="_blank" title="Click to know more about DISPLACEMENT">DISPLACEMENT</a> and the applied force are in the same upward direction then, the angle betweeen them is `theta=0^(@)`. Since, `cos0^(@)=1and\|vecF_(a)\|=mgand\|dvecr\|=dr` <br/> `U=mgunderset(0)oversethintdrimpliesmg[r]_(0)^(h)=<a href="https://interviewquestions.tuteehub.com/tag/mgh-1095458" style="font-weight:bold;" target="_blank" title="Click to know more about MGH">MGH</a>`</body></html>