Question

One of the best movies ever was "2001: A Space Odyssey."

In the movie, the ape drops a bone on a planet, and you want to determine the mass of the planet. You have the following info:

Height of drop = 2 m

Time to drop = 1.02 s

Radius of planet = 3.39 million meters

What is the mass of the planet?

Answer 1

Using equation of the motion

H=ut+gt^2/2 ...1

Here H=2.0m , t=1.02 s u=0 ( the ape drops means rest)

, g is the gravity acceleration.

Put these values in equation 1

2.0=0+g(1.02)^2/2

g=4.0/1.02^2

g=3.84467512

g=3.845m/s^2

We know that the weight of the bone is equal to the Gravitational Force on the bone.

mg=GMm/R^2

M=gR^2/G. ...2

here g=3.845m/s^2 , R=3.39million meters =3.39×10^6 m

G=6.674×10^(-11) N.m^2/kg^2

put these values in equation 1

M=3.845×(3.39×10^6)^2/6.674×10^(-11)

M=6.62078581×10^23 Kg

M=6.62×10^23 kg. Answer