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Answer 1 · 2017-10-06T05:13:20

#2114" km"#

#F = G.m.M/(r^2)#

#color(red)(g=10m/s^2#

#color(green)(M = 6times10^24kg# (mass of the Earth)

#color(blue)(G = 6.7times10^-11 Nm^2kg^-2#

#color(orange)(m = 50kg#

#color(violet)(r=6.4*10^6m = 6341km# (Radius of earth)

Weight of #m=mg=50kg times10m/s^2=color(indigo)(500N#

We need to find #r'# such that #"Weight"= color(purple)(250N#
(half the weight of a 50kg mass)

#F = (G*m*M)/(r^2)#

#=>color(purple)(250N) = (color(blue)(6*10^-11)*color(green)(6*10^24)*color(orange)(50))/(r')^2= (1.8*10^16)/(r')^2#

#=>(r')^2=(1.8*10^16)/(250)=color(grey)(7.2*10^30#

#=>r'=sqrtcolor(grey)(7.2*10^30)~~8485281m~~color(blue)(8485km#

So, distance from earth's surface #=r'-r #
#=color(blue)(8485km-color(violet)(6341km))~~2114km#