Planet Mnqy has five times the mass of the earth and three times the diameter. Y
ID: 1965677 • Letter: P
Question
Planet Mnqy has five times the mass of the earth and three times the diameter. You may not look up the mass and radius of the earth for this problem. (A) Calculate gravitational acceleration near the surface of Mnqy using only the value for the gravitational acceleration near the surface of the earth. (B) A monkey weighs 100 N near the surface of Mnqy. Find the mass and weight of the monkey when he stands atop a mountain with an altitude equal to 10% of Mnqy’s radius.The answer is 5.45 m/s^2, 18.3 kg, 82.6
Explanation / Answer
gM/R^2 so if R increases by 3, then g decreases to 1/9th original value and if mass increases by 5, then g increases by 5 so g2=5/9*g1=9.8*5/9=5.44m/s^2. The monkeys mass is just 100N/5.44m/s^2=18.3kg regardless of altitude. If R increases by 10% to 3.3 earth, then g decreases by 1/(3.3^2) so g on the mountain is 4.5 m/s^2 and therefore weight is just 4.5*18.3=83N. Hope that helped!