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)

Explanation

g at height , `g_h=g/(1+h/R)^2`
In this problem , `g_h=50/100`g=0.5 g
0.5g= `g/(1+h/R)^2 rArr (1+h/R)^2 =g /(0.5g)=2`
`1+h/R = sqrt2, h/R =sqrt2-1 rArr` the height ,
h=0.414 R =0.414 x 6400 = 2650 km .