The small spherical planet called \"Glob\" has a mass of 6.12×1018 kg and a radi
ID: 1461432 • Letter: T
Question
The small spherical planet called "Glob" has a mass of 6.12×1018 kg and a radius of 5.72×104 m. An astronaut on the surface of Glob throws a rock straight up. The rock reaches a maximum height of 1.80×103 m, above the surface of the planet, before it falls back down. What was the initial speed of the rock as it left the astronaut's hand? (Glob has no atmosphere, so no energy is lost to air friction. G = 6.67×10-11 Nm2/kg2.) (in m/s)
A 25.0 kg satellite is in a circular orbit with a radius of 1.20×105 m around the planet Glob. Calculate the speed of the satellite. (in m/s)
A: 1.44×101 B: 2.09×101 C: 3.03×101 D: 4.39×101 E: 6.36×101 F: 9.22×101 G: 1.34×102 H: 1.94×102Explanation / Answer
mass M = 6.12×10^18 kg
radius R = 5.72×10^4 m
gravity of this planet g = GM/R^2 = 0.123 m/s^2
rock is thrown up.
rock max height h = 1.80 x 10^3 m
let u be initial speed of rock.
and final velocity at heightest point be v = 0
theen , v^2 - u^2 = 2gh
0 - u^2 = 2 x 0.123 x 1.8 x 10^3
u = 2.09 x 10^1 m/s
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b) R' = height of satellite
G as in question
M = planet mass
mv^2/R' = GMm/R'^2 (centrifugal force = gravitational force)
v^2 = GM/R'
v = sqrt(GM/R') = 5.83 x 10^1
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