At what height from the surface of Earth the gravitational force will be reduced by 10% if the radius of Earth is 6400 km?

At what height from the surface of Earth the gravitational force will

1.	At what height from the surface of Earth the gravitational force will be reduced by 10% if the radius of Earth is 6400 km?
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> :Gravitational <a href="https://interviewquestions.tuteehub.com/tag/force-22342" style="font-weight:bold;" target="_blank" title="Click to know more about FORCE">FORCE</a> on the Earth surface<br/>`F_(s)=(GMm)/(R_(E)^(2))` <br/>Gravitational force at <a href="https://interviewquestions.tuteehub.com/tag/height-1017806" style="font-weight:bold;" target="_blank" title="Click to know more about HEIGHT">HEIGHT</a> h<br/>`F_(h)=(GMm)/((R_(E)+h)^(2))` <br/>`<a href="https://interviewquestions.tuteehub.com/tag/therefore-706901" style="font-weight:bold;" target="_blank" title="Click to know more about THEREFORE">THEREFORE</a>(F_s)/(F_h)=((R_(E)+h)^(2))/(R_(E)^(2))=(10)/(9)` <br/>`3(R_(E)+h)=3.162R_(E)` <br/>`3h=(3.162-3)R_(E)` <br/>`=0.162R_(E)` <br/>`(R_(E)+h)/(R_E)=(3.162)/(3)` <br/>`therefore` Height h `=(0.162xx6400)/(3)` <br/>(or) h = 345.6 <a href="https://interviewquestions.tuteehub.com/tag/km-1064498" style="font-weight:bold;" target="_blank" title="Click to know more about KM">KM</a></body></html>