Question

Question #aa1f0

Answer 1

`2114" km"`

Explanation:

`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`