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gravitational field strength

The mass of earth is 81 times the mass of the moon.The radius of earth is 4 times the radius of moon.What is the gravitational field strength on the Earth's surface?
Original post by wanaaaaaaaa
The mass of earth is 81 times the mass of the moon.The radius of earth is 4 times the radius of moon.What is the gravitational field strength on the Earth's surface?


It seems that the question need to give the gravitational field strength of the surface of the moon.

Express the gravitational field strength on the Earth's surface in terms of the mass of the moon and radius of the moon. You should get
gE = k gm
Reply 2
Avatar for wanaaaaaaaa
wanaaaaaaaa
OP
3
How can i get the value of k?
Reply 3
Avatar for Ajmaster
Ajmaster
6
g is proportional to M/R^2 therefore If you let g be constant and equal to the gravitational strength of the moon, calculate how g gets affected when you alter M and R. If the mass is 81 times the moon's then you can tell that g of the Earth is now 81G. Now if R on Earth is 4 times of that of the Moon, then you need to take into account the inverse square relationship. Therefore 1/(4R)^2 = 1/16R^2, Therefore you need to divide the current value of Earth's g by 16. So g on Earth is 81g/16. This is the answer I woud hope.
Reply 4
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wanaaaaaaaa
OP
3
Yeah true. Thank you. I got it now.

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