Calculate the height at which the value of acceleration due to gravity becomes 50% of that at the surface of the earth. (Radius of the earth =6400 km )

Calculate the height at which the value of acceleration due to gravity

1.	Calculate the height at which the value of acceleration due to gravity becomes 50% of that at the surface of the earth. (Radius of the earth =6400 km )
Answer» Solution :g at HEIGHT , `g_(H)=g/((1+h/R)^2)` In this PROBLEM , `g_(h)=50/100g = 0.5 g` `0.5g =g/((1+h/R)^2)IMPLIES(1+h/R)^2=g/(0.5g)=2` `1+h/R=sqrt2,h/R=sqrt2-1implies` the height , `h = 0.414 R = 0.414 xx 6400 = 2650` km.