Suppose that the force on a 1kg mass on the surface of the earth is 10N and that the radius of the earth is about 600 km. Then the force on an 8kg mass placed at a point 2000 km from the center of the earth will be?
F=GmMR2F =G\frac{mM}{R^2}F=GR2mM
for a mass of 1 kg on the ground:\text{for a mass of 1 kg on the ground:}for a mass of 1 kg on the ground:
F1=10NF_1 = 10NF1=10N
R1=600km=6∗105mR_1=600km=6*10^5mR1=600km=6∗105m
F1=GM(6∗105)2F_1=G\frac{M}{(6*10^5)^2}F1=G(6∗105)2M
for a mass of 8 kg at a distance of 2000 km\text{for a mass of 8 kg at a distance of 2000 km}for a mass of 8 kg at a distance of 2000 km
from the center of the earth:\text{from the center of the earth:}from the center of the earth:
R2=2000km=2∗106mR_2= 2000km = 2*10^6mR2=2000km=2∗106m
F2=G8M(2∗106)2F_2=G\frac{8M}{(2*10^6)^2}F2=G(2∗106)28M
F2=8F1(6∗105)2(2∗106)2=7.2NF_2=8F_1\frac{(6*10^5)^2}{(2*10^6)^2}=7.2NF2=8F1(2∗106)2(6∗105)2=7.2N
Answer:7.2N\text{Answer:}7.2NAnswer:7.2N
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