12. How far from the earth’s surface does the acceleration due to gravity become 16% of it value on the surface of earth ? Given : R = 6400 km. [Ans. 9600 km]
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Step-by-step explanation:
The acceleration due to gravity is given by the below equation,
g=GMr2
Where G=6.67⋅10−11m3kg⋅s2 is the gravitational constant, M is the mass of the earth, and r is the distance to the Earth’s sentence. When the acceleration due to gravity is 16% of its value on the surface of the earth ( gsurface=9.82ms2 ) we know that,
Step-by-step explanation:
The acceleration due to gravity is given by the below equation,
g=GMr2
Where G=6.67⋅10−11m3kg⋅s2 is the gravitational constant, M is the mass of the earth, and r is the distance to the Earth’s sentence. When the acceleration due to gravity is 16% of its value on the surface of the earth ( gsurface=9.82ms2 ) we know that,
0.16⋅gsurface=GMr2
Rearranging we get,
r=GM0.16⋅gsurface−−−−−−−√
Thus, we get,
r=6.67⋅10−11m3kg⋅s2⋅5.972⋅1024kg0.16⋅9.82ms2−−−−−−−−−−−−−−−−√=15922346.88562m
Therefore, the acceleration due to gravity is 16%, of what it is on the surface of the Earth, at a distance of 15.922,347km.