Question 350.
A spaceship lands on an unknown planet. To determine the characteristics of this planet, a 1.30kg wrench is dropped from 5.00 m above the ground which hits the ground 0.811s later. The circumference of the planet is 62,400 km.
a) What is the mass of the planet, in kg?
b) Express the planet's mass in terms of the earth's mass.
Answer 350.
a)
Gravitational attraction between the planet and the wrench is
GMm/R^2 = mg
=> GM/R^2 = g
=> M = gR^2/G ... ( 1 )
For motion of the wrench,
5 = (1/2) g * (0.811)^2
=> g = 15.20 m/s^2
Radius of the planet,
R = (6.24 x 10^7)/(2π)
Plugging values of g and R in ( 1 ),
M = (15.20) * (6.24 x 10^7/2π)^2 / (6.67 x 10^-11) kg
= 2.25 x 10^25 kg
b)
Earth's mass = 5.9742 x 10^24 kg
=> planet's mass in terms of earth's mass
= 2.25 x 10^25 / 5.9742 x 10^24
= 3.76.
Link to YA!
A spaceship lands on an unknown planet. To determine the characteristics of this planet, a 1.30kg wrench is dropped from 5.00 m above the ground which hits the ground 0.811s later. The circumference of the planet is 62,400 km.
a) What is the mass of the planet, in kg?
b) Express the planet's mass in terms of the earth's mass.
Answer 350.
a)
Gravitational attraction between the planet and the wrench is
GMm/R^2 = mg
=> GM/R^2 = g
=> M = gR^2/G ... ( 1 )
For motion of the wrench,
5 = (1/2) g * (0.811)^2
=> g = 15.20 m/s^2
Radius of the planet,
R = (6.24 x 10^7)/(2π)
Plugging values of g and R in ( 1 ),
M = (15.20) * (6.24 x 10^7/2π)^2 / (6.67 x 10^-11) kg
= 2.25 x 10^25 kg
b)
Earth's mass = 5.9742 x 10^24 kg
=> planet's mass in terms of earth's mass
= 2.25 x 10^25 / 5.9742 x 10^24
= 3.76.
Link to YA!
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