Question

show the gravitational potential energy on the earth surfaceis v=-GMuponR where v=0 and r is equal to infinity​

Answer 1

$At a point inside the solid sphere: V </p><p>inside</p><p> </p><p> = </p><p>2R </p><p>3</p><p> </p><p>−GM</p><p> </p><p> (3R </p><p>2</p><p> −x </p><p>2</p><p> )</p><p>V </p><p>inside</p><p> </p><p> =−GM( </p><p>2R</p><p>3</p><p> </p><p> − </p><p>2R </p><p>3</p><p> </p><p>r </p><p>2</p><p> </p><p> </p><p> ); (if x=R) </p><p>At a point on the surface of the solid sphere:V </p><p>surface</p><p> </p><p> = </p><p>R</p><p>−GM</p><p> </p><p> ; (If x=R)</p><p>At a point outside the solid sphere:V </p><p>outside</p><p> </p><p> = </p><p>x</p><p>−GM</p><p> </p><p> ; (If x=R)</p><p>At the centre: x=0</p><p>⇒V </p><p>c</p><p> </p><p> =− </p><p>2</p><p>3</p><p> </p><p> </p><p>R</p><p>GM</p><p> </p><p> = </p><p>2</p><p>3</p><p> </p><p> V </p><p>surface</p><p> </p><p> in case of solid sphere potential is maximum at centre.</p><p>We have,</p><p>Gravitational potential on Earth =V</p><p>Now,</p><p>Gravitaional potential at the centre of the Earth =V </p><p>C</p><p> </p><p> = </p><p>2</p><p>3</p><p> </p><p> V </p><p>surface</p><p> </p><p> = </p><p>2</p><p>3</p><p> </p><p> V$