Question #220916

Question 2 options:

Given the value for the universal gravitational constant, the average value for the acceleration due to gravity at the surface of Earth, and the radius of Earth, Earth’s mass is ____x1024kg


1
Expert's answer
2021-07-28T03:56:02-0400

We have, acceleration due to gravity,


g=GMR2g = \frac {GM} {R2}


Where, G = Gravitational constant


= 6.67×1011N.m2/kg2,6.67×10^{-11} N.m^2/kg^2,


R = radius of the Earth = 6.4×106m6.4×10^6 m ,


g = acceleration due to gravity on Earth surface


= 9.8 m/s2 and M is the mass of Earth, then, we can write,


9.8=6.67×1011×M(6.4×106)29.8 = 6.67×10^{-11} ×\frac {M} {(6.4×10^6)^2}


=> 9.8=M×0.16284×10239.8 = M×0.16284×10^{-23}


So, mass of Earth = 9.8(0.16284×1023)kg\frac {9.8} {(0.16284×10^{-23} ) kg}


= 5.97×1024kg5.97×10^{24} kg


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