physics problem help please?
Planet X has two times the DIAMETER and three times the mass of the earth. What is the ratio gX : ge of gravitational acceleration at the surface of planet X to the gravitational acceleration at the surface of the Earth?
MASS of earth: 5.97x10^24kg
RADIUS of earth: 6.37x10^6 m
please help.
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X has twice the DIAMETER, hence twice the radius, of Earth; since force varies inversely with the square of distance, this will cut the gravitational force by 4.
X has three times the MASS; since force varies directly with mass, this will multiply the force by 3.
The net result is that gX : ge = 3 : 4.
Alternatively, consider
gX : ge = (Gm(3Me)/(2Re)²) : GmMe/(Re)²
m, G, Me and (Re)² cancel:
gX:ge = 3/4 : 1 = 3 : 4