Calculate the height at which the value of acceleration due to gravity becomes 50% of that at 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 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)/(100)g = 0.5g` `0.5 g = (g)/((1+(h)/(R))^(2)) rArr (1+(h)/(R))^(2) = (g)/(0.5 g) = 2` `1+(h)/(R) = sqrt(2), (h)/(R) = sqrt(2) - 1 rArr` the height, `h = 0.414 R = 0.414 xx 6400 = 2650km`.