I've been stuck on this equation for a while and I don't know if i'm missing a key part to the equation.. i just need help!

If the gravitational field strength at the top of Mount Everest is 9.772 N/kg, approximately how tall (in feet) is the mountain?

F= g ( m1 x m2)/ radius^2

f= gravitational force
g= 6.67x10^-11
m= mass
d= radius^2
earth mass= 5.98x10^24
earth radius = 6.38x10^6

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  1. You know that at sea level

    GM/r^2 = 9.8

    Since G and M don't change, at radius R at the mountain top,

    GM/R^2 = 9.772

    so, R^2/r^2 = 9.8/9.772 = 1.0028653
    R = 1.0014316r
    R-r = 0.0014316r = 9134m

    That seems a bit high. Better check my math.

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  2. The actual height of Everest is 8848 m. Your number is close, and you used the right method. The difference is probably due to the use of too few significant figures for G(or GM/r^2).

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